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A   COLLECTION 


OF 


MATHEMATICAL  AND  PHYSICAL 


TABLES 


FROM 


A  COURSE  OF  EXPERIMENTS  IN  PHYSICAL  MEASUREMENT. 


BY 

HAROLD   WHITING,   PH.D., 

ASSISTANT  PROFESSOR  OF  PHYSICS   IN  THE  UNIVERSITY  OF  CALIFORNIA. 


BOSTON,   U.S.A. 
D.  C.  HEATH   AND  CO.,  PUBLISHERS. 

1900. 


A   COLLECTION 


OF 


MATHEMATICAL  AND  PHYSICAL 


TABLES 


FROM 


A  COURSE  OF  EXPERIMENTS  IN  PHYSICAL  MEASUREMENT. 


BY 

HAROLD   WHITING,   Pn.IX, 

ASSISTANT  PROFESSOR  OF  PHYSICS   IN  THE  UNIVERSITY  OF  CALIFORNIA. 


BOSTON,   U.S.A. 
D.   C.  HEATH   AND  CO.,  PUBLISHERS. 

1900. 


Copyright, 
BY  HAROLD  WHITING. 


JOHN  WILSON  AND  SON,  CAMBRIDGE,  U.S.A. 


PREFACE. 


THESE  mathematical  and  physical  tables  with  their 
explanations  have  been  reprinted  from  plates  of  a 
work  on  "  Physical  Measurement "  (pages  761-900, 
Part  III.) ,  prepared  by  the  author  while  holding  the 
position  of  Instructor  in  Physics  at  Harvard  Univer- 
sity. In  accordance  with  a  practical  suggestion  con- 
tained in  a  review  of  this  work,1  four-place  tables 
of  logarithms  and  antilogarithms  were  subsequently 
introduced  (pages  821  a,  b,  c,  d) ;  but  it  was  not 
thought  desirable  to  omit  the  five-place  tables,  which 
are  preferred  by  many  persons  even  for  rough  and 
rapid  work. 

It  will  be  noticed  that  the  most  important  mathe- 
matical tables  extend  from  1  to  11  units,  instead  of 
stopping  in  the  usual  manner  at  10.  By  this  slight 
extension  ten-fold  accuracy  becomes  attainable  in  the 
use  of  factors  between  1.0  and  1.1,  which  are  of  com- 
paratively frequent  occurrence  in  physical  calculations. 

The  physical  tables  are  arranged  especially  for 
scientific  use,  and  are  expressed  accordingly  in  the 
Metric,  —  or,  more  precisely,  in  the  Centimetre-Gram- 
Second  (C.  G.  S.)  system,  now  widely  adopted  by 

1  "  Philosophical  Magazine,"  October,  1891,  page  396. 


116 


iv  PREFACE. 

scientific  men.  This  system  has  one  great  advantage 
over  all  others,  in  that  it  is  the  only  one  system 
which  has  been  consistently  applied  to  all  branches  of 
physics.  Feet  and  pounds  are,  it  is  true,  more  com- 
monly employed  by  English-speaking  people  than 
metres  and  grams  ;  but  the  volt,  ohm,  and  ampere  are 
familiar  to  every  electrician,  while  the  corresponding 
units  of  the  English  system  are  practically  unheard  of. 
The  Metric  system  is  preferred  also  by  many  persons  on 
account  of  the  facility  of  the  reductions  from  absolute 
to  practical  units,  or  the  reverse,  which  in  the  Metric 
system  consist  simply  in  moving  a  decimal  point. 
The  necessary  decimal  multipliers  are  generally  given 
in  connection  with  each  value  or  column  of  values 
contained  in  the  tables.  Engineers  will  find  factors 
for  reducing  English  to  Metric  values,  or  the  reverse, 
on  the  last  three  pages,  and  will  note  that  a  single 
setting  of  a  "  slide  rule  "  is  sufficient  for  the  rapid 
conversion  of  a  long  series  of  data. 

The  author  has  sought  to  embrace  in  the  physical 
tables  all  the  properties  of  substances  about  which 
sufficient  information  could  be  obtained.  To  make 
this  possible,  it  was  found  necessary  to  employ  a  con- 
densed arrangement  (see  pages  843-863),  whereby  a 
dozen  or  more  properties  of  a  given  substance  could 
be  represented  in  a  single  line.  It  was  not  thought 
desirable  to  include  in  the  tables  rare  substances,  or 
those  of  variable  or  uncertain  composition,  unless  in 
addition  to  densities,  boiling-points,  etc.,  necessary  to 
identify  such  substances,  a  determination  of  at  least 
two  other  physical  properties  could  be  found. 


PREFACE.  V 

Various  sources  of  authority  for  the  values  con- 
tained in  these  tables  are  mentioned  on  pages  794- 
795.  Care  has  been  taken  to  give  all  figures  in  regard 
to  which  different  physicists  were  found  to  agree,  and 
in  general  one  and  only  one  additional  figure,  express- 
ing some  more  or  less  probable  mean  among  the 
several  determinations.  Attention  is  called  to  the 
fact  that  in  this  respect  the  author  has  departed  from 
the  usual  misleading  custom  of  appending  two  or 
more  insignificant  figures  to  results  (see  page  796), 
and  that  most  of  the  differences  which  will  be  found 
between  values  quoted  in  this  book  and  those  given 
elsewhere  are  due  to  this  departure.  It  is  hoped, 
accordingly,  that  throughout  the  physical  tables,  in 
the  absence  of  any  special  warning  to  the  contrary, 
it  may  be  reasonably  safe  to  count  upon  the  accuracy 
of  every  figure  except  the  last. 

BERKELEY,  March  11,  1892. 


TABLE    OF    CONTENTS. 


MATHEMATICAL    AND    PHYSICAL    TABLES. 


PAGE 

EXPLANATION  OF  TABLES 761 

SOURCES  OF  AUTHORITY 794 


MATHEMATICAL    TABLES. 

TABLE 

1.  PROPORTIONAL  PARTS 797 

2.  POWERS,  CIRCULAR  PROPERTIES,  ETC 798 

3.  TRIGONOMETRIC  FUNCTIONS  (S-PLACE) 800 

3A.    RECIPROCALS .     .  802 

3C.    SQUARES     . 804 

3D.    CUBES 806 

3F.    CIRCUMFERENCES  OF  CIRCLES 808 

3G.    AREAS  OF  CIRCLES 810 

3H.    VOLUMES  OF  SPHERES 812 

4.  NATURAL  SINES 814 

4A.    LOGARITHMIC  SINES 816 

5.  NATURAL  TANGENTS 818 

5A.    LOGARITHMIC  TANGENTS 820 

5B.    ANTILOGARITHMS 821a 

5C.    LOGARITHMS  (4-PLACE) 821c 


viii  TABLE  OF  CONTENTS. 


6.  LOGARITHMS  (5-PLACE) 822 

7.  PROBABILITY  OF  ERRORS     .      .  842 


PHYSICAL  TABLES. 
GENERAL  PROPERTIES  OF  SOLIDS,  LIQUIDS,   AND  GASES. 

8.  PROPERTIES  OF  ELEMENTARY  SUBSTANCES    .     .     .     843 

9.  PROPERTIES   OF    SOLIDS  —  BUILDING    MATERIALS, 

ETC. 846 

9a.  PROPERTIES  OF   SOLIDS  —  CHEMICAL  MATERIALS, 

ETC 848 

10.  PROPERTIES    OF    SOLIDS  —  OPTICAL    MATERIALS, 

ETC 852 

11.  PROPERTIES   OF   LIQUIDS 856 

12.  PROPERTIES  OF  GASES  AND  VAPORS    ...          .     861 


HYPSOMETRIC,     HYGROMETRIC,    AND     BAROMETRIC 
TABLES. 

13a.  MAXIMUM  PRESSURE  OF  VAPORS 864 

14.  BOILING  POINTS  OF  WATER,  68  CM.  TO  80  CM.      .  867 
14A.  DEW-POINT,  TEMPERATURE,  AND  HUMIDITY     .     .  867 

15.  HYGROMETRIC  TABLE .868 

15A.  SPECIFIC  HEAT  OF  MOIST  AIR 868 

15B.  VELOCITY  OF  SOUND 869 

15C.  COEFFICIENTS  OF  INTERDIFFUSION  OF  GASES  .     .  869 

16.  REDUCTION  OF  BAROMETRIC  RKADTNGS  TO  CM.    .  870 
16  A.  (REDUCTION  OF  BAROMETRIC  READINGS  )  G  =  980  871 
16B.  j     TO  MEGADYNES  PER  SQ.  CM.       .     .      j  G  =  981  871 

17.  ESTIMATION  OF  HEIGHTS  BY  THK  BAROMETER     .  871 
17A.  CORRECTION  FOR  TEMPERATURE  IN  TABLE  17      .  871 
17B.  CORRECTION  FOR  HUMIDITY  JN  TABLE  17  ...  871 
18a.  BAROMETRIC  CORRECTIONS  FOR  EXPANSION     .     .  872 
ISb.  BAROMETRIC  CORRECTIONS  FOR  CAPILLARITY.     .  872 
18c.  BAROMETRIC      CORRECTIONS      FOR      MERCURIAL 

VAPOR 872 

18d.  REDUCTIONS  OF  DENSITY  TO  76  CM 873 

18e.  REDUCTIONS  OF  DENSITY  TO  0° 873 

18f.  REDUCTIONS  OF  VOLUME  TO  76  CM 873 

18g.  REDUCTIONS  OF  VOLUME  TO  0° 873 


TABLE   OF  CONTENTS.  ix 


REDUCTION    OF    WEIGHINGS    TO    VACUO. 

19.  DENSITY  OF  AIR  (0°- 30°;   72-77  CM.)      ....  874 

20.  CORRECTIONS  *OK  HUMIDITY  IN  TABLE  19      .     .  874 
20A.   BUOYANCY  OF  AIR  ON  BRASS  WEIGHTS       .     .     .  874 

21.  REDUCTION  OF  APPARENT  WEIGHINGS  TO  VACUO  875 


SPECIFIC  VOLUMES  AND   DENSITIES. 

22.  APPARENT  SPECIFIC  VOLUMES  OF  WATER   .     .     .  875 

23.  TRUE  SPECIFIC  VOLUME  OF  WATER 876 

23A.  TRUE  SPECIFIC  VOLUME  OF  MERCURY    ....  876 

23B.  APPARENT  SPECIFIC  VOLUME  OF  MERCURY     .     .  876 

2t.  DENSITY  OF  MERCURY 877 

25.  DENSITY  OF  WATER 877 

26.  DENSITY  OF  COMMERCIAL  GLYCERINE     .  877 


PROPERTIES  OF  SOLUTIONS  DEPENDING   UPON 
THEIR  STRENGTH. 

27.  DENSITY  OF  ALCOHOL  (0%-1 00%;    15°-22°)     .     .  878 

28.  DENSITY  OF  ACIDS  AND  SOLUTIONS  AT  15°      .     .  880 

29.  BOILING-POINTS  OF  SOLUTIONS 882 

30  SPECIFIC  HEATS  OF  SOLUTIONS 883 

31A.   ELECTRICAL  CONDUCTIVITY  OF  SOLUTIONS  AT  18°  884 

31 B.    REFRACTIVE  INDICES  OF  SOLUTIONS 885 

310.    TABLE  FOR  MIXING  SOLUTIONS 885 

31  D.   COEFFICIENTS  OF  SALINE  DIFFUSION 885 

31 K.     (  ROTATION  OF  THK  PLANE  OF  )  IN  SOLUTIONS  .  886 

31 F.     (      POLARIZATION,  LINES  A-H  i  IN  SOLIDS     .     .  886 


MISCELLANEOUS    DATA. 

31G.  MAGNETIC  ROTATION  OF  POLARIZATION.     ...  887 

31H.  MAGNETIC  SUSCEPTIBILITY,  ETC 887 

311.     COEFFICIENTS  OF  HYDRAULIC  FRICTION      ...  887 

31J.    COEFFICIENTS  OF  FRICTION  BETWEEN  SOLIDS.     .  887 

31K.   RELATIVE  RADIATION,  ABSORPTION,  ETC.     .     .     .  887 

31L.    CONSTANTS  OF  RADIATION .  887 

32a.     HEATS  OF  COMBUSTION  IN  OXYGEN 808 

32b.    HEATS  OF  COMBUSTION  IN  CHLORINE      ....  888 

33.      HEATS  OF  COMBINATION 888 


TABLE  OF  CONTENTS. 


ELECTROMOTIVE    FORCE    AND    RESISTANCE. 

34.  CONTACT  DIFFERENCES  OF  POTENTIAL    ....  889 

35.  ELECTROMOTIVE  FORCES  OF  VOLTAIC  CELLS  .     .  890 

36.  ELECTROMOTIVE  FORCE  AND  LENGTH  OF  SPARK  .  890 
37a.  SPECIFIC  RESISTANCES  OF  CONDUCTORS  ....  891 
37b.  SPECIFIC  RESISTANCES  OF  INSULATORS   ....  891 
38.  SPECIFIC  RESISTANCES  OF  ELECTROLYTES   .     .     .  891 


ARBITRARY    SCALES. 

39.  FAHRENHEIT   AND    CENTIGRADE   THERMOMETERS  892 

40.  HYDROMETER  SCALES 892 

41.  WAVE-LENGTHS 892 

42a.  BOARD  OF  TRADE  (IMPERIAL)  WIRE  GAUGE    .     .  893 

42b.    BIRMINGHAM  WIRE  GAUGE 893 

43.  MUSICAL  PITCH  893 


ASTRONOMICAL  AND  GEOGRAPHICAL  TABLES. 

44 A.  REDUCTION  OF  (')  AND  (")  TO  (°) 894 

44B.  EQUATION  OF  DATHS  IN  DIFFERENT  YEARS    .     .  894 

44C.  GAIN  OF  SIDEREAL  TIME  . 894 

44D.  SIDEREAL  TIME  AT  GREENWICH,  NOON  ....  894 

44E.  SEMI-DIAMETER  OF  THE  SUN 894 

44F.  DECLINATION  OF  THE  SUN 895 

44G.  EQUATION  OF  TIME 895 

44H.  THE  SOLAR  SYSTEM  896 

45.  RIGHT  ASCENSIONS  AND  DECLINATIONS  OF  STARS  896 

46.  GEOGRAPHICAL    LATITUDES,     LONGITUDES,     AND 

ELEVATIONS 897 

47.  ACCELERATION  OF  GRAVITY 897 

48.  LENGTHS  OF  SECONDS  PENDULA          .          ...  897 


REDUCTION    OF    MEASURES    TO    AND    FROM    THE 
C.    G.    S.    SYSTEM. 

49a.    REDUCTIONS  INDEPENDENT  OF  "G" 898 

49b.    REDUCTIONS  FOR  "G"=980  AND  "G"=981  899 


50.      CONSTANTS  FREQUENTLY  REQUIRED 900 


USE  AND    EXPLANATION    OF    MATHEMATI- 
CAL  AND   PHYSICAL   TABLES. 

TABLE  1  consists  of  products  obtained  by  multiply- 
ing any  of  the  whole  numbers  (from  1  to  100)  in  the 
left-hand  column  of  either  half  of  the  table  by  the 
decimals  .1,  .2,  .3,  .4,  .5,  .6,  .7,  .8,  .9  at  the  head  of  the 
table.  The  decimal  part  of  the  product  is  rejected  in 
every  case,  the  units  being  increased  by  1  if  the  frac- 
tion is  .5  or  more.  The  table  is  useful  in  dividing 
differences  into  parts  proportional  to  the  numbers  1, 
2,  3,  4,  5,  6,  7,  8,  9,  whence  the  name  of  the  table. 
It  may  be  used  in  connection  with  any  of  the  tables 
which  follow.  Let  us  suppose  that  it  is  required  to 
find  the  sine  of  12°.34  in  Table  4,  page  814.  We  find 
the  sine  of  12°. 3  (in  the  line  with  12°  and  in  the  col- 
umn with  .3)  to  be  .2130,  while  the  sine  of  12°.4  is 
.2147.  The  first  number  (.2130)  is  too  small  ;  the 
second  (.2147)  is  too  great.  The  difference  between 
them  is  .0017,  or  17  units  in  the  last  place,  as  indi- 
cated by  the  nearest  number  in  the  column  of  differ- 
ences. If  0°.l  makes  a  difference  of  17  units,  0°.04 
should  make  a  difference  of  .04  -5-  0.1  X  17,  that  is, 
6.8  or  (nearly)  7  units  in  the  last  place.  The  xante 
result  may  be  found  by  seeking  in  Table  1  a  number 

12 


762  EXPLANATION  OF  TABLES.  [No.  1. 

opposite  the  difference  (17)  and  under  the  figure  (4) 
for  which  the  interpolation  takes  place.  The  result 
(7  units  in  the  last  place)  is  to  be  added  to  the  sine 
of  12°.3,  because  the  sines  increase  when  the  angles 
increase  —  in  other  words,  because  the  differences 
are  positive.  The  sine  of  12°.34  is  accordingly 
0.2130  +  .0007  =  0.2137. 

Again,  to  find  the  reciprocal  of  6.789,  by  Table  3  A, 
page  802,  we  observe  that  the  reciprocal  of  6.78  is 
.14749,  while  that  of  6.79  is  .14728.  The  difference 
between  these  reciprocals  is  —  .00021,  because  the  re- 
ciprocals decrease  as  the  numbers  increase.  Opposite 
21  and  under  .9  in  Table  1  we  find  19  ;  hence  the 
answer  is  .14749  —  00019  =  .14730.  If  we  had  used 
the  nearest  number  (22)  in  the  column  of  differences 
of  Table  3  A.,  instead  of  the  actual  difference  (21), 
we  should  have  found  similarly  .14729  instead  of 
14730.  The  true  reciprocal  happens  to  lie  between 
these  two  values. 

Table  1  can  be  used  also  in  inverse  processes. 
Let  us  suppose  that  it  is  required  to  find  the  cube 
root  of  800,  by  Table  3  D,  page  806.  We  notice 
that  the  cube  of  9.28  is  799.2,  just  below  800,  while 
the  cube  of  9.29  is -801.8,  just  above  800;  the  differ- 
ence being  26  units  in  the  last  place.  The  difference 
between  799.2  and  800.0  is  8  units  in  the  last  place. 
In  line  with  the  number  26  in  the  left-hand  column  of 
Table  1,  and  over  the  number  8,1  we  find  .3.  We  see 

1  When  the  exact  number  cannot  be  found  amongst  the  propor- 
tional parts  we  choose  the  one  nearest  to  it. 


No.  2.]  MATHEMATICAL  TABLES.  763 

therefore  that  the  cube  of   9.283  would  be   800.0 ; 
hence,  conversely,  9.283  is  the  cube  root  of  800. 

The  use  of  proportional  parts  is  especially  recom- 
mended when  accuracy  in  the  last  figure  is  important. 
The  tables  which  follow  have,  however,  been  con- 
structed with  such  fulness  that  interpolation  will 
generally  be  unnecessary,  or  readily  carried  on  in  the 
head. 

TABLE  2  contains  several  functions  often  needed, 
and  is  intended  for  rough  and  rapid  work.  More 
exact  values  of  the  functions  will  be  found  in  Tables 
3  A  —  3  H,  which  follow. 

Column  a  contains  the  "reciprocals"  of  the  num- 
bers in  the  first  column  from  1  to  100.  The  recipro- 
cal of  a  number  is  defined  as  the  quotient  obtained 
when  unity  is  divided  by  the  number  in  question. 
Example  :  the  reciprocal  of  30  is  .0333. 

Column  b  contains  the  square  roots  of  numbers 
from  1  to  100.  The  square  root  of  a  number  is  de- 
fined as  a  number  which  multiplied  by  itself  would 
give  a  product  equal  to  the  original  number.  Ex- 
ample :  the  square  root  of  49  is  7.00. 

Column  c  contains  the  squares  of  numbers  from  1 
to  100 ;  that  is,  the  products  obtained  when  each 
number  is  multiplied  by  itself.  Example  :  the  square 
of  40  is  1600. 

Column  d  contains  the  cubes  of  numbers  from  1  to 
100.  The  cube  of  a  number  is  defined  as  the  result 
of  multiplying  that  number  by  the  square  of  that  num- 
ber ;  or  as  the  result  of  multiplying  that  number  three 
times  into  unity.  Example  :  the  cube  of  5  is  125. 


764  EXPLANATION  OF  TABLES.  [No.  3. 

Column  e  contains  three-place  logarithms  (see  under 
Table  6)  from  0.1  to  10.0.  Example :  the  logarithm 
of  2  is  0.301,  correct  to  3  places  of  decimals. 

Column  f  contains  the  circumferences  of  circles 
having  diameters  from  .1  to  10.0.  The  circumference 
is  given  in  the  same  units  as  the  diameter.  Example  : 
given  the  diameter  2.0  cm.,  the  circumference  is 
6.28  cm. 

Column  g  contains  the  areas  of  circles  having  diam- 
eters from  .1  to  10.0.  The  area  is  given  in  units  cor- 
responding to  the  unit  of  length  employed  in  meas- 
uring the  diameter.  Example :  given  the  diameter 
2.0  cm.,  the  area  of  the  circle  is  3.14  sq.  cm. 

Column  h  contains  the  volumes  of  spheres  having 
diameters  from  .1  to  10.0.  The  volume  is  given  in 
units  corresponding  to  the  unit  of  length  employed 
in  measuring  the  diameter.  Example:  given  the 
diameter  2.0  cm.,  the  volume  of  the  sphere  is  4.19 
cu.  cm. 

TABLE  3  contains  principally  3-place  trigonometric 
functions,  and  is,  like  Table  2,  intended  for  rough 
and  rapid  work. 

Column  a  contains  angles  from  0°  to  90° ;  covering 
in  all  a  right-angle. 

Column  b  contains  the  tangents  of  angles.  The 
tangent  of  an  (acute)  angle  is  denned,  with  reference 
to  a  right-angled  triangle,  as  the  ratio  of  the  side 
opposite  it  to  the  (shorter)  adjacent  side.  Example  : 
the  tangent  of  15°  is  0.268. 

Column  c  contains  "  arcs ; "  that  is,  in  a  circle  of 
radius  unity,  the  length  of  the  arcs  intercepted  by 


No.  3.]  MATHEMATICAL   TABLES.  765 

angles  with  their  vertices  at  the  centre  of  the  circle. 
"Arcs"  are  also  called  the  "circular  measures"  of 
angles.  Example:  15°  is  equal  to  0.262 -in  circular 
measure ;  or  the  arc  of  15°  is  0.262. 

Column  d  contains  the  "  chords  "  of  angles.  The 
chord  of  an  angle  is  defined,  with  reference  to  an 
isosceles  triangle,  as  the  ratio  of  the  side  opposite  the 
vertical  angle  to  either  of  the  two  equal  sides.  Ex- 
ample :  the  chord  of  15°  is  0.261. 

Column  e  contains  natural  sines.  The  sine  of  an 
angle  is  defined,  with  respect  to  a  right-angled  tri- 
angle, as  the  ratio  of  the  side  opposite  that  angle  to 
the  longest  side,  or  hypothenuse.  Example :  the  sine 
of  15°  is  0.259. 

Column  f  contains  natural  cosines.  The  cosine  of 
an  angle  is  defined  as  the  sine  of  the  complement  of 
that  angle  (see  i).  Example :  the  cosine  of  15°  is 
0.966. 

Column  g  contains  rates  of  vibration  corresponding 
to  different  arcs  from  0°  to  45°,  through  which  for  in- 
stance a  pendulum  is  vibrating.  The  arcs  are  meas- 
ured from  one  side  of  the  vertical  to  the  other..  The 
rate  of  vibration  in  a  very  small  arc  is  taken  as  1. 
Example  I. :  if  a  pendulum  vibrates  once  a  second  in 
a  very  small  arc,  it  will  vibrate  .99893  times  a  second 
in  an  arc  of  15°  (i,  e.  7J°  on  each  side  of  the  verti- 
cal). Example  II. :  given  the  time  of  oscillation  of 
a  magnet  equal  to  10  seconds  in  an  arc  of  45° ;  re- 
quired its  time  of  oscillation  in  a  very  small  arc. 
Answer,  10  X  .99037  =  9.9037  sec.  Column  g  con- 
tains also  cover  sines  from  45°  to  90°. 


766  EXPLANATION  OF  TABLES.  [No.  3. 

The  coversine  of  an  angle  is  defined  as  unity  less 
the  sine  of  the  angle.  It  is  the  same  thing  as  the 
versine  of  the  complement  of  the  angle.  Versines 
and  coversines  measure  various  errors  introduced  into 
physical  measurement  when  two  lines  which  ought  to 
be  parallel  or  perpendicular  are  inclined  at  a  given 
angle.  The  inclination  of  the  two  lines  is  to  be 
found  in  column  a  or  in  column  i  as  the  case  may  be. 
Example  I. :  the  shaft  of  a  cathetometer  (^f  262) 
makes  an  angle  of  89°  with  the  horizon  ;  required 
the  error  introduced  in  the  measurement  of  vertical 
distances.  Answer,  .00015  parts  in  1,  or  ^f  Q  of  1  %. 
Example  II. :  a  magnet  which  should  be  horizontal 
dips  10°;  required  the  error  in  estimating  its  mag- 
netism. Answer,  .0152,  or  1  ffa  oj0. 

Column  h  contains  secants,  or  the  reciprocals  of 
cosines.  Example  :  the  secant  of  15°  is  1.035. 

Column  i  contains  the  complements  of  the  angles 
contained  in  column  a  ,  that  is,  the  results  of  sub- 
tracting these  angles  from  90°.  Example  :  the  com- 
plement of  15°  is  75°. 

It  may  be  remarked  that  the  cotangent  of  an  angle 
is  the  tangent  of  its  complement ;  the  cochord  of  an 
angle  is  the  chord  of  its  complement ;  the  cosecant  of 
an  angle  is  the  secant  of  its  complement.  These  may 
all  be  found,  accordingly,  by  Table  3.  Examples :  — 

The  cotangent  of  15°  =  tangent  of  75°  =  3.732 
The  cochord  of  15°  =  chord  of  75°  =  1.218 
The  cosecant  of  15°  =  secant  of  75°  =  3.864 

To  find  any  function  of  the  complement  of  an  angle, 


No.  3F.]  MATHEMATICAL  TABLES.  767 

we  have  only  to  look  up  that  angle  in  column  i,  in- 
stead of  in  column  a. 

TABLE  3  A  is  essentially  a  4-place  table  of  recipro- 
cals from  1.00  to  11.09,  carried  out,  however,  to  5 
places  between  6.00  and  9.99.  Examples:  the  re- 
ciprocal of  2.73  is  .3663 ;  the  reciprocal  of  273  is 
.003663. 

TABLE  3  C  is  a  4-place  table  of  squares  from  1.00 
to  9.99,  carried  out  to  5  places  between  10.0  and 
11.09.  Examples :  the  square  of  3.14  is  9.860 ;  the 
square  of  31.4  is  986.0.  The  square  root  of  1.25  is 
is  1.12  nearly,  or  more  exactly,  1.118  (see  under 
Table  1). 

TABLE  3  D  is  a  4-place  table  of  cubes  from  1.00  to 
9.99,  carried  out  to  5  places  from  10.0  to  11.09.  Ex- 
amples :  the  cube  of  5.55  is  171.0 ;  the  cube  of  .555  is 
.1710.  The  cube  root  of  800  .is  9.283  (see  under 
Table  1). 

TABLE  3  F  contains  the  circumferences  of  circles 
with  diameters  (diam.)  varying  from  1000  to  10090 
by  10  units  at  a  time.  The  results  are  carried  out  to 
units.  The  differences  in  this  table  are  either  31  or 
32,  from  beginning  to  end.  The  mean  difference  is 
31.416.  Proportional  parts  corresponding  to  this 
mean  difference  are  printed  at  the  bottom  of  the 
table.  The  circumference  is  given  in  units  of  the 
same  magnitude  as  the  diameter.  Example  I.:  the 
circumference  of  a  circle  3600  cm.  in  diameter  is 
11310  cm.  Example  II. :  given  a  circumference 
10,000  metres,  the  diameter  is  3180  metres,  nearly  ; 
or  more  exactly,  3183  metres  (see  under  Table  1). 


768  EXPLANATION  OF  TABLES.  [No.  4  A. 

TABLE  3  G  is  a  4-place  table  containing  the  areas 
of  circles  corresponding  to  diameters  (diam.)  from 
10.0  to  100.9.  The  area  is  given  in  units  correspond- 
ing to  the  unit  of  length  in  which  the  diameter  is 
measured.  Example  I. :  diameter  =  15.0  cm.,  area 
—  176.7  sq.  cm.  Example  II. :  diameter  =  55.5  mm., 
area  =  2419  sq.  mm.  —  24.19  sq.  cm.  Example  III. : 
area  =  4000  sq.  cm.,  diameter  =  71.4  cm.,  nearly ; 
more  exactly,  71.36  cm.  (see  under  Table  1). 

TABLE  3  H  contains  the  volumes  of  spheres  cor- 
responding to  diameters  from  1.00  to  10.09.  The 
volume  is  given  in  units  corresponding  to  the  unit  of 
length  in  which  the  diameter  is  measured.  Example 
I. :  diameter  =  11.1  mm.  =  1.11  cm. :  volume  — 
.539  cu.  cm.  =  539  cu.  mm.  Example  II. :  volume  = 
35.00  cu.  cm.,  diameter  =  4.06  cm.,  nearly ;  or  more 
exactly,  4.058  cm.  (see  under  Table  1). 

TABLE  4  is  a  4-place  table  giving  the  natural  sines 
of  angles  from  0°.0  to  89°.9.  when  interpreted  in  the 
ordinary  manner  by  means  of  the  argument  at  the  left 
and  at  the  top  of  the  page.  Natural  cosines  may 
also  be  found  by  means  of  this  table,  by  using  the 
argument  at  the  right  and  at  the  bottom  of  the  page. 
Example  I. :  the  sine  of  30°.0  is  0.5000.  Example 
II. :  the  cosine  of  30°.0  is  .8660. 

TABLE  4  A  is  a  4-place  table  giving  the  logarithmic 
sines  (that  is  the  logarithms  of  the  sines)  of  angles 
from  0°.0  to  89°. 9,  when  read  in  the  ordinary  way. 
Logarithmic  cosines  may  be  found  through  the  ar- 
gument at  the  right  and  bottom  of  the  page.  Ex- 
ample I.:  the  logarithm  of  the  sine -of  30°  is  1.6990. 


No.  6.J  LOGARITHMS.  769 

Example  II. :  the  logarithm  of  the  cosine  of  30°  is 
1.9375. 

TABLE  5  contains  the  natural  tangents  of  angles 
from  0°.0  to  89°.9.  Natural  cotangents  from  45°.0  to 
89°.  9  may  also  be  found  by  using  the  argument  at 
the  right  and  bottom  of  the  first  half  of  the  table. 
Below  this  limit,  they  are  not  given ;  but  they  may 
be  found  by  calculating  the  complement  of  the  angle 
and  looking  up  its  tangent.  Example  I. :  the  tan- 
gent of  30°  is  0.5774.  Example  II. :  the  cotangent 
of  22°.5  =  tangent  of  77°.5  =  4.511. 

TABLE  5  A  is  a  4-place  table  giving  the  loga- 
rithmic tangents  (that  is,  the  logarithms  of  the  tan- 
gents) of  angles  when  read  in  the  ordinary  way. 
Logarithmic  cotangents  may  also  be  found  by  using 
the  argument  at  the  right  and  at  the  bottom  of  the 
page.  Example  I. :  the  logarithm  of  the  tangent  of 
30°.0  is  1.7614.  Example  II. :  the  logarithm  of  the 
cotangent  of  30°  is  0.2386. 

TABLE  6  is  a  5-place  table  of  the  logarithms  of 
numbers  from  1,000  to  11,009.  A  decimal  point 
is  understood  after  the  first  figure  of  each  number 
and  before  the  first  figure  of  each  logarithm.  Ex- 
ample :  the  logarithm  of  2.000  is  .30103. 

When  the  decimal  point  of  a  number  does  not 
follow  the  first  figure,  the  corresponding  logarithm 
consists  of  two  parts.  The  first  part  is  a  whole 
number  called  the  u  characteristic  "  of  the  logarithm  ; 
the  second  or  decimal  part  is  called  the  "  mantissa." 

The  "  characteristic "  of  a  logarithm  is  not  to  be 
found  in  Table  6,  but  is  to  be  supplied  by  inspection. 


770  EXPLANATION  OF  TABLES.  [No.  6. 

Its  numerical  value  is  equal  to  the  number  of  figures 
between  the  decimal  point  of  the  argument  and  the 
space  following  the  first  figure  of  the  argument. 

Thus  the  logarithm  of  the  number  1.11  has  the 
characteristic  0;  while  the  characteristics  of  11.1 
and  111  are  1  and  2  respectively.  The  sign  of  the 
characteristic  is  positive  if  the  decimal  point  is  at  the 
right  of  the  first  figure  of  the  argument ;  if  it  is  at 
the  left,  the  sign  is  negative.  Thus  the  characteris- 
tic of  the  logarithm  of  .1111  is  —  1.,  the  character- 
istic of  the  logarithm  of  .01111  is  —  2.,  &c.  The 
negative  sign  is  in  practice  written  over  the  char- 
acteristic, as  it  affects  this  characteristic  alone. 

It  is  a  peculiarity  of  logarithms  that  the  "man- 
tissa "  is  not  affected  by  the  location  of  the  decimal 
point  in  the  original  number.  The  logarithm  of 
1.111  (namely,  0.04571)  is,  for  instance,  the  same  as 
the  logarithm  of  1,111.  (namely,  3.04571),  as  far  as 
the  mantissa  is  concerned.  The  mantissa  or  decimal 
part  of  the  logarithm  of  any  number  may  be  found, 
accordingly,  by  Table  6,  by  considering  only  the  fig- 
ures of  which  the  number  is  composed. 

Initial  and  final  ciphers  may  be  thrown  off  ad  libi- 
tum in  this  process ;  but  ciphers  in  the  middle  of  a 
number  form  an  essential  part  of  it.  Thus  in  finding 
the  decimal  part  of  the  logarithm  of  .000,100,100, 
we  need  to  consider  only  the  figures  1001,  since  these 
are  preceded  and  followed  only  by  ciphers ;  but  the 
ciphers  between  the  first  and  last  figures  cannot  be 
neglected.  The  following  logarithms  from  Table  6 
may  also  serve  as  examples :  — 


No.  6.]  LOGARITHMS.  771 

The  logarithm  of  3.1416  is  0.49715 

"  "         "   980  u  2.99123 

"         u    41,700,000  "  7.62014 

"  .00367  "  3.56467 

Conversely,  in  finding  the  number  corresponding  to  a 
a  given  logarithm,  we  first  obtain  the  figures  of  which 
the  number  is  composed  by  considering  simply  the 
mantissa,  or  decimal  part  of  the  logarithm,  and  to 
these  figures  we  add  as  many  initial  or  final  ciphers 
as  may  be  needed  ;  then  starting  with  the  space  at 
the  right  of  the  first  figure  (disregarding  initial 
ciphers)  we  count  off  to  the  right  if  the  characteristic 
of  the  logarithm  is  positive  (or  to  the  left  if  negative) 
a  number  of  spaces  equal  to  the  characteristic  in  ques- 
tion, in  order  to  locate  the  decimal  point.  In  any 
case  the  number  of  figures  between  the  decimal 
point  and  the  space  following  the  first  figure  of  the 
answer  must  be  equal  to  the  characteristic  of  the 
logarithm. 

Example  I. :  given  the  logarithm  0.14860,  the  fig- 
ures of  the  corresponding  number  are  1408 ;  the  char- 
acteristic of  the  logarithm  being  0,  the  answer  is  1.408. 
Example  II. :  given  the  logarithm  3.14860,  the  man- 
tissa being  .14860  as  before,  we  find  the  same  figures, 
1408.  Since  the  characteristic  (3)  is  positive,  the 
decimal  point  is  at  the  right  of  the  first  figure,  and 
since  3  figures  must  come  between  the  decimal  point 
and  the  space  following  the  first  figure,  the  answer  is 
1,408. 


772  EXPLANATION  OP  TABLES.  [No.  6. 

The  following  rules  embody  the  most  important 
applications  of  logarithms,  —  namely,  to  problems  of 
multiplication  and  division. 

Rule  1.  To  multiply  two  or  more  numbers  to- 
gether, find  the  logarithm  of  each  and  add  the  loga- 
rithms together.  The  number  corresponding  to  their 
sum  is  the  required  product.  Example  :  to  multi- 
ply 2X4. 

The  logarithm  of  2  is  0.30103 

"          u  "   4  is  0.60206 

The  sum  of  these  logarithms  is  0.90309, 

which  is  the  logarithm  of  8,  the  answer.  Numbers 
involving  more  than  3  significant  figures  may  be  mul- 
tiplied together  by  the  aid  of  logarithms  with  greater 
ease  than  by  arithmetical  processes. 

Rule  2.  To  divide  one  number  by  another,  find 
the  logarithm  of  the  first,  subtract  the  logarithm  of 
the  second ;  the  remainder  is  the  logarithm  of  the 
answer.  Example  :  to  divide  4  by  8, 

The  logarithm  of  4  is  0.60206 

"          "          "    8  "  0.90309 

The  difference  is         T.69997, 

which  is  the  logarithm  of  0.5,  the  answer. 

Rule  3.  To  find  the  value  of  a  fraction  with  sev- 
eral factors,  find  the  logarithm  of  each  factor  in  the 
numerator,  and  add  the  logarithms  together.  Then 
find  the  logarithm  of  each  term  in  the  denominator, 
and  add  these  logarithms  together.  Subtract  the 


No.  7.]  LOGARITHMS.  773 

latter  sum  from  the  former  sum.  The  remainder  is 
the  logarithm  of  the  answer.  Example  :  to  find  the 
value  of  the  fraction 

.2345  X  45.67  x  6,789   wefind_ 
1.234  X  34,56  X  567.8' 

(1)  log.  .2345  =  1.37014     (5)  log.  1.234  =  0.09132 

(2)  "    45.67  =  1.65963     (6)    «     34.56  =  1.53857 

(3)  "      6789  =  3.83181      (7)    "     567.8  =  2.75420 
(4). sum  =  4.86158      (8)  sum  =  4.38409 

(9)  subtract         4.38409 

(10)  remainder^  0.47749  =  log.  3.002  +,  ans. 

Rule  4.  To  raise  a  number  to  any  power,  find  its 
logarithm,  multiply  by  the  power,  and  the  product  is 
the  logarithm  of  the  answer.  Example  :  to  find  the 
4th  power  of  2.  The  logarithm  of  2  is  0.30103; 
which  multiplied  by  4  gives  1.20412.  This  is  the 
logarithm  of  16,  the  answer. 

Rule  5.  To  extract  any  root  of  a  number,  find 
the  logarithm  of  the  number  and  divide  by  the  root 
in  question ;  the  quotient  is  the  logarithm  of  the 
answer.  Example :  to  find  the  12th  root  of  2.  The 
logarithm  of  2  is  0.30103  ;  this  divided  by  12  gives 
.02509,  which  is  the  logarithm  of  1.0595,  the  answer. 
(This  is  the  value  of  the  interval  called  1  semitone 
on  the  tempered  scale.) 

TABLE  7  contains  the  probability  of  an  error's  ex- 
ceeding limits  bearing  to  the  "  probable  error  "  (§  50) 
the  ratios  represented  in  the  left-hand  column.  The 
probability  is  expressed  as  so  many  chances  in  1. 
Example  I. :  the  probable  error  of  a  weighing  is  1 


774  EXPLANATION  OF   TABLES.  [Nos.  8-12. 

centigram  ;  what  are  the  chances  of  an  error  greater 
than  1  centigram?  Answer,  by  definition,  an  even 
chance  or  0.50000.  Example  II. :  under  the  same 
circumstances,  what  are  the  chances  of  an  error's  ex- 
ceeding 2  centigrams?  Answer,  0.17734,  i.  e.  17,734 
chances  in  100,000,.  or  about  1  chance  in  6.  Exam- 
ple III. :  under  the  same  circumstances,  what  are 
the  chances  of  an  error's  exceeding  5  centigrams  ? 
Answer,  0.00075,  or  less  than  1  in  1000.1 

TABLES  8,  9,  10,  11,  and  12  contain  (1)  the  names, 
(2)  the  chemical  symbols,  and  (3)  the  atomic  weights 
of  various  substances,  and  deal  with  the  following 
physical  properties :  (4)  the  specific  gravity  (§  69)  of 
gases  and  vapors  referred  to  hydrogen  at  the  same 
temperature  and  pressure ;  (5)  the  density  (§  15) 
of  substances  at  0°  under  the  ordinary  atmospheric 
pressure ;  (6)  the  "  viscosity "  of  liquids  at  about 
20°,  or  the  force  in  dynes  required  to  maintain  a 
relative  velocity  of  1  cm.  per  sec.  between  two  sur- 
faces 1  cm.  square  and  1  cm.  apart ;  (7)  the  "  surface 
tension  "  of  liquids  (^  169)  at  about  20°,  or  the  force 
in  dynes  with  which  each  surface  of  a  liquid  film 
1  cm.  broad  tends  to  contract ;  (8)  the  "  breaking 
strength  "  of  solids,  or  the  force  in  kilo-megadynes 2 
required  to  break  a  wire  1  sq.  cm.  in  cross  section  ; 
(9)  the  "  crushing  strength  "  of  solids,  or  the  force 
in  kilo-megadynes  required  to  crush  a  block  1  sq.  cm. 

1  The  chances  relate  only  to  "accidental  errors"  (§  24).      The 
chances  of  "  mistakes  "  are  not  included. 

2  1  kilo-megadyne  =  1  02  "  tonne  weight,"  or  1  English  ton  weight, 
nearly 


Nos.  8-12.]  GENERAL  PROPERTIES.  775 

in  cross  section ;  (10)  the  "  shearing  strength  "  of 
solids,  or  the  force  in  kilo-megadynes  required  to  cut 
a  wire  1  sq.  cm.  in  cross  section;  (11)  the  "hard- 
ness "  of  -solids  according  to  Mohs'  arbitrary  scale 
(page  587)  ;  (12)  the  "  simple  rigidity  "  of  solids,  or 
the  force  in  kilo-megadynes  required  to  make  two 
surfaces  1  cm.  square  and  1  cm.  apart  move  parallel 
to  one  another  through  a  thousandth  of  a  centimetre 
(.001  cm)  ,  (13)  "  Young's  modulus,"  or  the  force  in 
kilo-megadynes  required  to  pull  two  such  surfaces 
apart  through  one  thousandth  of  a  centimetre  (.001 
cm)  ;  (14)  the  "  resilience  of  volume  "  or  the"  pres- 
sure in  kilo-megadynes  required  to  compress  a  centi- 
metre cube  by  one  cubic  millimetre  ;  (15)  the  average 
cubical  "  coefficient  of  expansion"  of  substances1 
(§  83)  between  0°  and  100°  under  a  constant  pres- 
sure of  76  cm.  of  mercury  ;  (16)  the  "  melting-point " 
of  solids,  or  the  "freezing-point"  of  liquids  on  the 
Centigrade  scale  :  (17)  the  u  boiling-point "  of  liq- 
uids, or  the  "  temperature  of  condensation  "  of 
vapors  at  the  atmospheric  pressure  ;  (18)  the  "  criti- 
cal temperature"  of  liquids  and  vapors,  —  that  is,  the 
temperature  at  which  the  properties  of  the  liquid  and 
its  vapor  become  indistinguishable ;  (19)  the  "  criti- 
cal pressure  "  of  liquids  and  vapors,  that  is  the  pres- 
sure of  the  vapor  of  a  liquid  at  the  critical  tempera- 
ture in  megadynes  per  sq.  cm.;  (20)  the  "pressure 

1  When  a  change  of  state  takes  place  between  0°  and  100°,  the 
averages  in  question  refer  only  to  that  part  of  the  interval  (0°  to 
100°)  in  which  the  substance  exists  in  the  state  named  at  the  head 
of  the  table. 


776  EXPLANATION  OF  TABLES.  [Xos.  8-12. 

of  vapors  "  at  20°,  in  megadynes  per  sq.  cm. ;  (21) 
the  average  specific  heat  of  substances1  (§  86)  be- 
tween 0°  and  100°,  under  the  "  constant  pressure  " 
of   76  cm.  of  mercury;    (22)   the   average   specific 
heat  of  substances1  between  0°  and  100°,  when  pre- 
vented from  expanding ;  that  is,  confined  to  a  "  con- 
stant volume;  "  (23)  the  "  latent  heat  of  melting  "  of 
solids,  or  the  "latent  heat  of  liquefaction"  of  liquids; 
that  is,  the  number  of  units  of  heat  required  to  con- 
vert 1  gram  of  a  solid,  at  its  melting-point,  into  a  liquid 
at  the  same  temperature  under  a  pressure  of  1  atmos- 
phere ;  (24)  the  "  latent  heat  of  vaporization  "  of  liq- 
uids, or  the  "  latent  heat  of  condensation''  of  vapors  ; 
that  is,  the  number  of  units  of  heat  required  to  con- 
vert 1  gram  of   a   liquid  at   the   boiling-point  into 
vapor  at  the  same  temperature  under  the  atmospheric 
pressure ;  (25)  the  "  heat  conductivity"  of  substances, 
or  the  number  of  units  of  heat  conducted   in  one 
second  between  two  opposing  faces  of  a  centimetre 
cube  differing  1°  in  temperature  ;  (26)  the  "  electri- 
cal conductivity"  of  substances,   or  the  current  in 
amperes  flowing  between  two  opposing  faces  of  a  cen- 
timetre cube  differing  1  microvolt  (.000,001  volt)  in 
electrical  potential  (§  139)  ;  (27)  the  "  thermo-elec- 
tric heights"  of  conductors,  or  the  electromotive  force 
in  microvolts  developed  by  a  thermo-electric  junction 
of  which  one  element  is  lead,  corresponding  to  a  dif- 
ference of  temperature  of  1°  ;  (28)  u  electro-chemical 
equivalents,"   or  the  weight  in  milligrams  of  various 

1  See  footnote,  page  775. 


Nos.  8-12.]  GENERAL  PROPERTIES.  777 

elementary  substances  affected  by  a  current  of  10  am- 
p£res  in  1  second  ;  (29)  the  specific  inductive  capacity 
of  substances  determined  by  currents  alternating 
several  hundred  times  per  second  (^[  256)  ;  (30)  the 
minimum  "  extraordinary  index  of  refraction  "  of  opti- 
cal materials  ;  (31)  the  "ordinary  index  of  refraction" 
of  uniaxial  crystals,  or  the  "  medium''  index  of  refrac- 
tion of  biaxial  crystals ;  (32)  the  maximum  "  extraor- 
dinary index  of  refraction  "  of  different  substances  — 
these  three  indices  referring  to  the  sodium  (D)  line ; 
(33)  the  ordinary  (or  medium)  "  index  of  disper- 
sion," or  the  difference  between  the  ordinary  (or 
medium)  indices  of  refraction  for  the  lines  A  and  H 
of  the  solar  spectrum ;  and  finally  (34)  the  solubility 
of  solids  in  water,  expressed  in  per-cents  by  weight, 
and  the  solubility  of  gases,  also  in  per-cents  by 
weight,  under  a  pressure  of  1  atmosphere. 

The  first  line  of  each  table  contains  factors  by 
which  the  values  given  in  the  column  below  them 
may  be  reduced  to  the  c.  G.  s.  system.  Thus  the  co- 
efficient of  resilience  of  aluminum  (Table  8)  is  0.5  (?) 
X  1012  =  500,000,000,000(7),  and  the  thermo-electric 
height  of  copper  is  about  4  x  100  =  400  absolute 
units. 

TABLE  8  contains  the  properties  of  elementary 
substances. 

TABLE  9  contains  the  properties  of  solids  remark- 
able especially  for  their  strength  or  for  other  proper- 
ties rendering  them  suitable  for  building  materials  or 
for  the  construction  of  machines. 


778  EXPLANATION  OF  TABLES.  [No,  14  A. 

TABLE  9  A  contains  the  properties  of  certain 
chemical  salts  and  other  substances  in  ordinary  use. 

TABLE  10  contains  the  properties  of  solids  remark- 
able for  their  optical  or  other  allied  properties. 

TABLE  11  contains  properties  of  liquids. 

TABLE  12  contains  properties  of  gases  and  vapors. 

TABLES  13  A,  B,  and  C,  give  the  (maximum)  pres- 
sure in  megadynes  per  sq.  cm.  of  the  vapor  arising 
from  various  liquids  at  different  temperatures. 

TABLE  13  A  contains  substances  which  are  for  the 
most  part  gaseous  at  ordinary  temperatures. 

TABLE  13  B  contains  more  or  less  volatile  liquids. 

TABLE  13  C  gives  the  pressure  of  the  vapor  of 
mercury,  sulphur,  and  water,  including  the  vapor 
of  water  arising  from  sulphuric  acid  of  different 
strengths. 

TABLE  13  D  contains  the  "  density  of  steam,"  or 
the  maximum  density  of  aqueous  vapor  at  different 
temperatures. 

TABLE  14  gives  the  boiling-points  of  water  corres- 
ponding to  different  barometric  pressures  from  68.0 
to  77.9  centimetres  of  mercury  reduced  to  latitude 
45°  (see  Landolt  and  Bornstein,  Table  20).  Exam- 
ple :  when  the  barometer  stands  at  75.0  cm.,  water 
boils  at  99°.63. 

TABLE  14  A  gives  dew-points  (calculated  from 
Regnault's  data)  corresponding  to  different  degrees  of 
temperature  and  "  relative  humidity."  The  ''dew- 
point"  means  that  temperature  at  which  moisture 
would  (barely)  be  precipitated  out  of  the  air  (as 
when  dew  is  formed)  ;  the  "  relative  humidity  "  is  the 


No.  16  A.]  METEOROLOGICAL  DATA.  779 

proportion  which  the  moisture  contained  in  the  air  at 
a  given  temperature  bears  to  the  maximum  possible 
amount  which  it  can  hold  at  that  temperature.  Ex- 
ample I. :  the  air  of  a  room  at  20°  is  half  saturated 
with  moisture  (i.  e.  the  relative  humidity  =  50  %); 
required  the  dew-point.  Answer,  9°  Centigrade  by 
Table  14  A.  Example  II. :  sea  air  saturated  at  9° 
with  moisture  is  warmed  to  20° ;  required  the  rela- 
tive humidity.  Answer,  50  %. 

TABLE  15  shows  at  a  given  temperature  (T)  the 
maximum  pressure  (P)  of  aqueous  vapor  in  centi- 
metres of  mercury,  the  maximum  density  (D)  of 
aqueous  vapor,  and  the  factor  (F)  by  which  the  differ- 
ence between  the  readings  of  a  wet  and  a  dry  bulb 
thermometer  must  be  multiplied  in  order  to  find  the 
difference  between  the  dew-point  and  the  tempera- 
ture (T)  of  the  air.  The  data  have  been  taken  from 
Kohlrausch,  Table  13,  Landolt  and  Bornstein,  Tables 
18  a  and  23,  and  from  Everett's  "  Units  and  Physical 
Constants,"  Art.  124.  The  first  three  columns  are  an 
amplification  of  results  contained  in  Table  13.  The 
last  column  is  useful  in  hygrometry.  Example :  if 
the  dry-bulb  thermometer  reads  20°,  and  the  wet-bulb 
thermometer  reads  15°,  so  that  the  difference  be- 
tween them  is  5°,  we  have  (since  F  =  1.8),  5°  X  1.8 
=  9°,  which  subtracted  from  20°  gives  11°  for  the 
dew-point. 

TABLE  16  A  gives  the  specific  heat  of  moist  air  at 
about  50°,  corresponding  to  different  dew-points  un- 
der a  constant  pressure  of  76  cm.  of  mercury.  The 
specific  h,eat  of  dry  air  at  0°  (.2383)  is  the  mean  be- 


780  EXPLANATION  OF  TABLES.  [No.  16  B. 

tween   the    results    obtained    by   Regnault   and   E. 
Wiedemann.     The  other  specific  heats  have  been  cal- 

*  culated  by  interpolation  between  the  specific  heats  of 
air  and  of  steam  (.4805). 

'  TABLE  15  B  gives  the  velocity  of  sound  in  atmos- 
pheric air, calculated  for  different  degrees  of  temper- 
ature and  relative  humidity,  allowing  for  the  effect  of 
moisture  on  the  density  of  air  and  on  the  ratio  of  the 
two  specific  heats  of  air  under  constant  pressure  and 
under  constant  volume.  The  barometric  pressure 
(which  has  hardly  a  perceptible  influence  on  the  re- 
sult) was  assumed  to  be  76  cm.  of  mercury. 

TABLE  15  C  contains  coefficients  of  interdiffusion 
of  gases.  The  values  (due  to  Maxwell)  are  taken 
from  Everett's  "Units  and  Physical  Constants"  (Art. 
131).  If  two  reservoirs  filled  with  different  gases 
are  connected  by  a  tube  1  cm.  long,  the  numbers  in 
Table  15  C  show  the  mean  velocity  in  cm.  per  sec. 
wi'th  which  a  stream  of  gas  flows  through  the  tube 
from  each  reservoir  into  the  other. 

TABLE  16  is  intended  for  the  reduction  of  baro- 
metric readings,  when  given  in  inches,  to  centimetres. 
The  last  line  of  the  table  contains  "  proportional 
parts"  (see  under  Table  1). 

TABLES  16  A  and  B  are  intended  for  the  reduction 
of  barometric  readings  in  cm.  of  mercury  at  0°  to  meg- 
adynes  per  sq.  cm.  A  is  calculated  for  a  value  of  the 
acceleration  of  gravity  (#)  equal  to  980  cm.  per  sec.  per 
sec. ;  B  for  the  value  g  =  981.  The  two  tables  differ 
by  about  10  units  in  the  last  place.  For  values  of  g 
between  980  and  981,  or  just  outside  of  these  limits, 


No.  18  a.]  BAROMETRIC  TABLES.  781 

results  may  be  easily  obtained  by  interpolation.  Ex- 
ample :  g  =  980.4 ;  required  the  value  of  1  atmos- 
phere (76  cm.)  in  megadynes  per  sq.  cm.  Answer, 
1.0126  +  11  x  -4  =  1.0130  megadynes  per  sq.  cm. 

Table  17  gives  the  elevation  in  metres  above 'the 
sea-level  corresponding  to  different  barometric  pres- 
sures at  10°  Centigrade.  It  has  been  calculated  for 
dry  air  in  latitude  45°  by  the  formula 

h  =  190790  (log.  76— log.  p)  (1  +  .000,0001  A). 

It  is  used  in  estimating  heights  by  the  barometer. 
Example  I. :  the  mean  barometric  pressure  is  70.0 
cm.  at  the  top  of  a  hill  rising  out  of  the  sea,  the  sides 
of  the  hill  having  a  mean  temperature  of  about  10° ; 
required  the  height  of  the  hill.  Answer,  about  681 
metres.  Example  II.  :  the  barometric  pressures  at 
a  given  instant  are  75.1  cm  at  the  foot  of  a  hill,  and 
74.2  cm.  at  the  top  of  the  hill,  —  the  mean  temperature 
being  about  10° ;  required  the  height  of  the  hill. 
Answer,  199  —  99  =  100  metres. 

TABLES  17  A  and  17  B  give  corrections  in  per 
cent  to  be  added  to  or  subtracted  from  the  results  of 
Table  17,  according  to  the  mean  temperature  and 
dew-point  between  the  observing  stations.  Thus  for 
a  mean  temperature  23°  and  the  dew-point  +  8°  add 
4.6  +  0.4  —  5.0  %  to  all  results.  This  would  make 
the  height  of  the  hill  in  Example  II.,  105  (instead  of 
100)  metres. 

TABLE  18  a  gives  the  correction  in  centimetres  to 
be  subtracted  (on  account  of  expansion)  from  the 
reading  of1  a  mercurial  barometer  provided  with  a 


782  EXPLANATION  OF  TABLES.  No.  18  c,J 

brass  scale  reaching  from  its  zero  in  the  surface  of 
mercury  in  the  reservoir  to  the  free  surface  of  mer- 
cury in  the  tube.  In  calculating  this  table,  the  coeffi- 
cient of  expansion  of  mercury  was  assumed  to  be 
.000180  +  .000,000,036*;  the  value  .000019  was 
taken  for  the  coefficient  of  expansion  of  brass.  Ex- 
ample I. :  the  mercurial  column  is  76  cm.  long,  meas- 
ured by  a  brass  scale,  its  temperature  is  20°,  we 
subtract  0.245  cm.,  and  find  75.755  cm.  for  the  value 
at  0°.  Example  II. :  same  as  I.  except  that  a  glass 
scale  is  used ;  corrected  value  the  same  less  .016  cm.T 
that  is,  75.739  cm. 

TABLE  18  b  gives  the  mean  correction  to  be  added 
to  the  apparent  height  of  the  mercurial  column  on  ac- 
count of  "  capillarity,"  that  is,  the  tendency  of  capil- 
lary or  in  general  small  tubes  to  depress  a  mercurial 
column  (see  Everett,  46  A,  and  Pickering,  Table  12) » 
The  correction  depends,  however,  not  only  upon  the 
internal  diameter  of  the  barometer  tube  at  the  point 
where  the  mercury  stands,  but  also  upon  the  height 
of  the  "  meniscus,"  which  is  different  according  to 
the  direction  in  which  the  mercurial  column  has 
been  moving.  Corrections  corresponding  to  differ- 
ent heights  of  the  meniscus  are  taken  from  Kohl- 
rausch,  Table  15,  6th  ed.  The  results  in  this 
table  differ  widely  from  those  quoted  in  the  2d 
edition. 

TABLE  18  c  contains  corrections  for  the  pressure  of 
mercurial  vapor.  They  have  been  obtained  by  aver- 
aging the  results  of  Regnault,  Hagen,  and  Hertz, 
quoted  in  Landolt  and  Bornstein,  Table  27.  The 


[No.  20.  DENSITY  OF  GASES.  783 

results  in  question  differ  in  some  cases  even  in  regard 
to  the  position  of  the  decimal  point. 

On  account  of  the  great  discrepancy  between  the 
results  obtained  by  different  observers,  barometric 
readings,  even  when  corrected  by  Tables  18  a,  18  6, 
and  18  0,  are  significant  only  as  far  as  hundredths  of 
a  centimetre. 

TABLES  18  d,  18  e,  18  /,  and  18  #,  contain  factors 
for  the  reduction  of  either  the  density  or  the  volume 
of  a  gas  to  0°  or  to  76  cm.  Example  I. :  the  density 
of  coal-gas  being  .0005  at  20°  and  75.0  cm.,  required 
its  density  at  0°  and  76  cm.  Answer,  .0005  X  1.0734 
X  1.0133  =  .00054+.  Example  II. :  the  volume  of 
a  gas  at  20°  and  75  cm.  is  100  cu.  cm. ;  required  its 
volume  at  0°  and  76  cm.  Answer,  100  X  0.9316 
X  0.9868  =  91.9  cu.  cm.  If  the  gas  were  collected 
over  water  at  20°  we  should  subtract  1.74  cm.  (see 
Table  15)  from  the  apparent  pressure  (75  cm.)  and 
find  73.26  cm.  for  the  pressure  of  the  gas.  This 
would  give  a  factor  .9640  instead  of  .9868,  and  a 
result  89.8  cu.  cm.  in  the  example  above. 

TABLE  19  contains  the  density  (or  weight  of  1 
cu.  cm..)  of  air  corresponding  to  different  tempera- 
tures and  pressures,  and  has  been  taken  from  Kohl- 
rausch,  2d  ed.,  Table  6.  It  was  calculated  from 
Regnault's  observations  for  latitude  45°. 

TABLE  20  contains  corrections  for  the  results  in 
Table  19  to  be  applied  on  account  of  moisture.  Ex- 
ample :  required  the  density  of  air  at  20°  and  76  cm. 
pressure  when  the  dew-point  is  +  4°  Centigrade. 
Answer,  .001204  —  .000004  =  .001200. 


784  EXPLANATION  OF  TABLES.  [No.  23. 

TABLE  20  A  contains  the  weight  of  air  displaced 
by  1  gram  of  brass  of  the  density  8.4,  and  is  useful 
in  calculating  effective  weights  (§  64).  Example:  a 
body  is  balanced  by  100  grams  of  brass  in  air  of  the 
density  .001200  ;  required  the  effective  weight  of  the 
body.  Answer,  100  grams  minus  100  X  0.000143 
grams,  or  99.9857  grams. 

TABLE  21  contains  factors  for  reducing  apparent 
weighings  with  brass  weights  to  vacuo.  The  factors 
correspond  to  different  densities  of  the  substance 
weighed,  as  well  as  of  the  air  in  which  the  weighing 
takes  place.  Example:  a  piece  of  glass  of  the  den- 
sity 2.5  is  balanced  by  100  grams  of  brass,  in  air  of 
the  density  .00120  ;  required  its  true  weight  in  vacuo. 
Answer,  100  X  1.00034  =  100.034  grams. 

TABLE  22  contains  "  apparent  specific  volumes  "  of 
water;  that  is,  the  space  in  cubic  centimetres  occupied 
by  a  quantity  of  water  weighing  apparently  1  gram 
when  counterpoised  in  air  with  brass  weights  of  the 
density  8.4.  The  apparent  specific  volumes  corres- 
pond to  different  temperatures  and  different  condi- 
tions of  atmospheric  density,  and  are  useful  especially 
in  calculations  of  volume  or  capacity  in  h}rdrostatics. 
Example :  a  flask  holds  apparently  1000  grams  (1 
litre,  nearly)  of  water  at  20°,  when  weighed  in  air  of 
the  density  .00120  ;  required  the  capacity  of  the  flask. 
Answer,  1000  X  1.00279  =  1002.79  cu.  cm. 

TABLE  23  contains  true  "  specific  volumes "  of 
water ;  that  is,  the  space  in  cubic  centimetres  occu- 
pied at  various  temperatures  by  a  quantity  of  water 
weighing  actually  1  gram  in  vacuo.  These  values 


No.  26.]  DENSITY  OF  LIQUIDS.  785 

are  reciprocals  of  those  in  Table  24,  and  are  to  be 
used  for  the  calculation  of  volumes  corresponding  to 
true  weights  in  vacuo.  Example :  a  piece  of  steel 
displaces  100  grams  of  boiling  water;  required  its 
volume.  Answer,  100  X  1.04311  =  104.311  cu.  cm. 

TABLE  23  A  gives  the  true  specific  volume  of  mer- 
cury at  different  temperatures,  and  is  used  like  Table 
23.  In  calculating  this  table  Regnault's  value 
(13.596)  for  the  density  of  mercury  at  0°  was  used,  and 
a  coefficient  of  expansion  .000180  +  .000,000,036  t. 

TABLE  23  B  gives  apparent  specific  volumes  of 
mercury  when  balanced  by  brass  weights  of  the  den- 
sity 8.4  in  air  of  the  density  .0012.  It  is  used,  like 
Table  22,  to  calculate  volumes  and  capacities.  Exam- 
ple :  the  apparent  weight  of  mercury  required  to  fill 
a  tube  at  20°  is  100  grams;  required  the  capacity 
of  the  tube.  Answer,  100  X  0.073812  =  7.3812 
cu.  cm. 

TABLE  24  contains  the  density  of  mercury  at  dif- 
ferent temperatures.  The  values  are  reciprocals  of 
those  contained  in  Table  23  A. 

TABLE  25  contains  the  density  of  water  at  differ- 
ent temperatures.  A  mean  value,  1.00001,  was  taken 
for  the  maximum  density  of  water  (Kupffer's  value  is 
1.000013).  The  relative  densities  lie  between  the 
estimates  of  Rossetti  and  Volkmann,  founded  upon 
observations  by  Despretz,  Hagen,  Jolly,  Kopp, 
Matthiessen,  Pierre,  and  Rossetti. 

TABLE  26  contains  the  density  of  commercial 
glycerine,  calculated  from  observations  made  in  the 
Jefferson  Physical  Laboratory. 


786        EXPLANATION  OF  TABLES.      [No.  31  A. 

TABLE  27  contains  the  density  of  dilute  alcohol 
corresponding  to  different  temperatures  and  different 
strengths.  The  values  are  a  mean  between  results 
obtained  by  numerous  observers. 

TABLE  28  gives  the  density,  at  15°,  of  acids  and 
saline  solutions  corresponding  to  various  strengths, 
and  is  useful  in  making  tests  with  a  densimeter.  See 
Storer's  "  Dictionary  of  Solubilities."  Example  :  the 
density  of  some  sulphuric  acid  is  1.807  at  (about) 
15°  ;  required  its  strength.  Answer  (about)  88  o/0 . 

TABLE  29  gives  the  boiling-points  of  solutions  of 
various  strengths  estimated  by  interpolation  from 
data  contained  in  Storer's  "  Dictionary  of  Solubilities." 
It  furnishes  an  independent  (and  in  processes  of  con- 
centration by  boiling  a  very  convenient)  method  of 
estimating  the  strength  of  such  solutions.  Thus  a 
solution  of  hydrate  of  sodium  boiling  at  120°  is 
known  to  have  a  strength  of  about  40  %. 

TABLE  30  gives  the  specific  heats  of  solutions  of 
different  strengths  at  about  20°.  It  is  useful  in  cer- 
tain processes  in  calorimetry  (see  ^f^[  99-100).  The 
numbers  were  obtained  by  interpolation  from  results 
contained  in  Landolt  and  .Bb'rnstein,  Tables  71  and  72. 
Those  nearest  the  observed  values  are  printed  in 
heavier  type. 

TABLE  31  A  gives  the  electrical  conductivity  of 
solutions  at  about  18°.  It  shows  the  current  in  am- 
peres which  an  electromotive  force  of  one  volt  would 
cause  to  flow  through  a  metre-cube  of  the  solutions  in 
question,  or  through  a  voltameter  with  plates  1  deci- 
metre square  and  1  cm.  apart,  filled  with  these  solu- 


tfo.  31  F.]  PROPERTIES  OF   SOLUTIONS.  787 

tions,  neglecting  the  effects  of  polarization.  The  re- 
sults must  be  multiplied  by  10-11  (.000,000,000,01) 
to  reduce  them  to  the  c.  G.  s.  system.  The  relative 
values  of  different  results  are  probably  accurate 
within  5  or  10  per  cent,  but  their  absolute  values  are 
much  less  reliable. 

TABLE  31  B  gives  Refractive  and  Dispersive  in- 
dices corresponding  to  the  sodium  (D)  line  for  solu- 
tions of  different  strengths,  and  was  obtained  by 
interpolation  from  results  quoted  by  Landolt  and 
Bornstein. 

TABLE  31  C  is  intended  to  facilitate  the  preparation 
of  solutions  of  any  desired  strength,  and  for  the  cal- 
culation of  per  cent  contents  from  the  ratio  of  two 
constituents.  Example :  how  many  parts  of  salt 
must  be  added  to  100  of  water  to  make  a  20  %  solu- 
tion ?  Let  A  =  salt ;  B  =  water,  —  the  answer  is 
25  parts.  Example  II. :  a  solution  contains  100  parts 
of  sulphuric  acid  to  150  of  water;  required  its 
strength.  Let  A  =  water,  B  =  sulphuric  acid  ;  the 
-answer  is :  60  %  water,  40  %  sulphuric  acid. 

TABLE  31  D  gives  coefficients  of  diffusion  of  saline 
solutions  in  water  at  about  20°.  The  values  were 
calculated  from  Graham's  data  quoted  in  Cooke's 
"  Chemical  Physics."  Example  :  how  much  common 
salt  would  escape  by  diffusion  into  pure  water  from  a 
20  °/0  solution  in  600,000  seconds  through  a  layer  1.2 
cm.  thick  and  8  sq.  cm.  in  cross  section  ?  Answer, 
20  %  of  600,000  X  8  X  .000,0046  -*- 1.2  =  3.68  grams. 

TABLES  31  E  and  F  give  the  rotation  in  degrees  of 
the  plane  'of  polarization  of  different  kinds  of  light 


788  EXPLANATION  OF  TABLES.  [No.  31  L. 

corresponding  to  the  Fraunhofer  lines  A  to  H.  E  re- 
fers to  dilute  solutions  having  such  a  depth  that  a 
beam  of  light  passing  through  an  orifice  1  cm.  square 
meets  just  one  gram  of  the  dissolved  substance.1  F 
refers  to  the  effect  of  plates  1  cm.  thick. 

TABLE  31  G  relates  to  the  effect  of  a  magnetic  field 
in  rotating  the  plane  of  polarization  of  light  parallel 
to  the  lines  of  force. 

TABLE  31  H  relates  to  (1)  Magnetic  Susceptibil- 
ity, (2)  Saturation,  and  (3)  Permanent  Magnetism, — 
that  is,  the  magnetic  moment  of  a  unit  cube  of  differ- 
ent materials  (1)  in  a  unit  magnetic  field,  (2)  in  an 
infinite  magnetic  field,  and  (3)  in  space  after  the 
magnetizing  influence  has  been  removed.  The  re- 
sults are  taken  from  Everett,  and  Ganot. 

TABLE  31  I  contains  some  of  Weisbach's  results  for 
the  coefficient  of  friction  of  water  moving  with  dif- 
ferent velocities  through  tubes  not  far  from  1  cm.  in 
diameter.  The  results  have  been  reduced  to  the 
the  c.  G.  s.  system. 

TABLE  31  J  gives  coefficients  of  friction  of  solids 
on  solids,  taken  from  De  Laharpe's  "  Notes  et  Form- 
ules  de  1'Inge'nieur." 

TABLE  31  K  contains  coefficients  of  reflection,  ab- 
sorption, and  transmission  of  radiant  heat,  from 
Ganot's  Physics. 

TABLE  31  L  contains  estimates  (by  the  author)  <  f 
the  heat  radiated  at  different  temperatures  by  1  sq. 

1  The  rotation  is  proportional,  within  more  or  less  narrow  limits,, 
to  the  strength  of  the  solution;  but  may  vary  widely  outside  of  these 
limits.  Cases  of  reversal  even  occur.  See  Landolt  and  Bornstein. 


No.  33.]  HEAT  OF   COMBUSTION.  78$ 

cm.  of  blackened  or  perfectly  radiating  surface  sur- 
rounded by  perfectly  absorbing  walls,  or  space  at  0°. 
The  table  was  calculated  by  the  formula  — 

q  =  log.-1  (.0013  X  (t°  +  273°)  — 1.8249)  —  .034, 

which  was  found  to  reconcile  various  well-known 
facts.  Example  :  how  much  heat  is  required  to  main- 
tain 1  sq.  cm.  of  platinum  at  its  melting-point  (1900°) 
for  1  sec.  ?  Answer,  10  (?)  units.1 

TABLES  32  A  and  32  B  give  heats  of  combustion2 
in  oxygen  and  in  chlorine  respectively,  from  data 
quoted  by  Everett,  by  Landolt  and  Bornstein,  and  by 
other  authorities.  The  chemical  reactions  are  not  in 
all  cases  such  as  actually  take  place ;  but  the  table 
gives  the  heat  which  it  is  supposed  would  be  developed 
if  the  reactions  did  take  place.  The  last  column 
gives  the  electromotive  forces  developed  by  or  neces- 
sary to  undo  some  of  the  reactions.  Example :  2 
grams  of  hydrogen  uniting  with  16.0  grams  of  oxy- 
gen give  out  69,000  units  of  heat,  or  34.500  units 
per  gram  of  hydrogen.  This  is  equivalent  to  1440 
megergs  per  mgr.  of  hydrogen  consumed.  To  de- 
compose water,  an  electromotive  force  of  1.49  volts 
is  required. 

TABLE  33  gives  "  heats  of  combination  "  involving 
more  complicated  chemical  reactions  than  those  which 
take  place  in  simple  combustion. 

1  This  corresponds  to  8  +  volt-amperes  per  candle-power. 

2  The  heat  of  combustion  of  many  substances  can  be  inferred  onl^r 
from  indirect  processes.     See  experiment  38. 


790  EXPLANATION  OF  TABLES.  [No.  38. 

TABLE  34  gives  contact  differences  of  electrical  po- 
tential in  volts.  The  data  are  taken  from  Everett's 
"Units  and  Physical  Constants,"  Art.  206.  Example  : 
a  piece  of  zinc  is  brought  into  contact  with  a  piece  of 
copper  ;  required  the  difference  of  electrical  potential. 
Answer,  the  zinc  is  positively  electrified  with  respect 
to  the  copper;  the  difference  of  potential  is  0.750 
volts. 

TABLE  35  gives  the  electromotive  force  in  volts  of 
voltaic  cells  of  various  sorts. 

TABLE  36  gives  the  relation  between  electromotive 
forces  and  the  length  in  mm.  of  the  spark  which 
they  produce  in  ordinary  atmospheric  air,  calculated 
from  Everett,  Art.  192.  Example:  an  induction 
machine  produces  sparks  2.5  mm.  long ;  required  the 
difference  of  potential  between  its  poles  at  the  in- 
stant. Answer,  9000  volts.  Only  the  first  two  fig- 
ures are  significant  in  this  answer. 

TABLES  37  a  and  b  give  specific  resistances  of  con- 
ductors and  insulators  at  0°.  The  last  column  gives 
the  per  cent  of  increase  of  all  these  resistances  due 
to  a  rise  of  temperature  of  1°  Centigrade. 

TABLE  38  gives  the  specific  resistances  of  electro- 
lytes corresponding  to  various  strengths.  The  resist- 
ances are  in  ohms,  and  apply  to  a  centimetre  cube  of 
the  liquid.  The  probable  error  of  the  results  is  about 
10  %.  Relative  values  are  probably  not  so  inaccurate. 
Example :  required  the  resistance  of  a  cubical  Dan- 
iell  cell,  with  a  plate  of  copper  10  X  10  cm.,  separated 
lay  a  layer  of  20  %  (crystallized)  sulphate  of  copper 
-5  cm.  deep,  and  by  a  layer  of  20  %  (crystallized)  sul- 


ffo.  43.]  ARBITRARY   SCALES.  791 

phate  of  zinc,  also  5  cm.  deep,  from  a  plate  of  zinc  10 
X  10  cm.  Answer :  the  resistance  of  the  copper  so- 
lution is  20  X  5  -^-  (10  X  10)  =  1  ohm  ;  that  of  the 
zinc  solution  is  the  same ;  hence  the  resistance  of  the 
battery  is  2  ohms. 

TABLE  39  gives  a  comparison  between  the  Fahren- 
heit and  Centigrade  thermometers.  Example:  98°. 6, 
F  =  37°.0,  C. 

TABLE  40  (Pickering,  Table  14)  gives  a  comparison 
of  hydrometer  scales.  Example :  40  Beaum6  for 
liquids  lighter  than  water  corresponds  to  the  density 
0.830. 

TABLE  41  gives  lengths  of  waves  of  light  in  air, 
intermediate  between  the  numerous  results  quoted 
by  Landolt  and  Bornstein.  The  probable  error  is 
about  1  unit  in  the  last  figure.  Example  :  the  Fraun- 
hofer  lines  Di  and  D2,  together  designated  ^  (or  D), 
are  due  to  sodium  (symbol,  Na)  and  occur  in  t^g  yellow 
of  the  spectrum.  They  correspond  to  numSlr  50  on 
Bunsen's  scale,  to  numbers  1003  and  1007  on  (Bun- 
sen  and)  KirchofFs  scale,  and  have  the  wave-lengths 
0.00005896  cm.  and  0.00005890  cm.  respectively. 

TABLE  42  A  refers  to  the  imperial  wire  gauge  adopt- 
ed by  the  Board  of  Trade  (Stewart  &  Gee,  I.  B.). 

TABLE  42  B  gives  the  Birmingham  wire  gauge 
(B.  w.  G.).  The  results  are  intermediate  between 
those  quoted  in  English,  French,  and  German  books. 
The  probable  error  is  about  1  unit  in  the  last  figure. 

TABLE  43  gives  the  number  of  vibrations  corres- 
ponding to  a  series  of  musical  notes  on  the  tempered 
or  isotonic  'scale,  one  half  of  a  semitone  apart.  The 


792  EXPLANATION  OF  TABLES.  [No.  44  C- 

designation  of  some  of  these  notes  is  given  in  the 
left-hand  or  in  the  right-hand  column.  The  former 
is  to  be  used  for  "physical  pitch,"  in  which  all 
powers  of  the  number  2  represent  the  note  C  ;  the 
right-hand  column  may  be  used  for  notes  given  by 
American  instruments  tuned  to  "  concert  pitch. " 
The  numbers  between  those  corresponding  to  a  given 
note  in  the  first  and  last  columns  may  be  taken  to 
represent  the  same  note  according  to  the  old  Stutt- 
gart standard  of  pitch  (A  =  440,  C  =  264).  Ex- 
ample :  the  "  middle  C  "  of.  an  American  piano  (in 
the  little  octave),  makes  about  135.6  vibrations  per 
second,  and  corresponds  to  C#  physical  pitch. 

TABLE  44  A  gives  reductions  of  minutes  and 
seconds  to  thousandths  of  a  degree.  The  num- 
ber of  minutes  is  first  sought ;  the  tenths  of  a 
degree  will  be  found  next  to  it.  Then  in  the 
same  section  of  the  table  (there  are  6  sections)  the 
nearest  number  of  seconds  is  found,  and  next  to 
it  the  hundredths  and  thousandths  of  a  degree.  Ex- 
ample :  23°27'13//  =  23°.  +  0°.4  +  0°.054,  nearly,  or 
23°.454. 

TABLE  44  B  gives  the  correction  to  be  added  to 
dates  in  different  years  to  compare  them  with  the 
year  1891.  Thus,  Jan.  1,  IGh.  Om.  Os.,  A.  M.,  1899; 
corresponds  to  Jan.  1,  lOh.  Om.  Os.  +  Ih.  29m.  28s. 
A.M.  =  Jan.  1,  llh.  29m.  28s.  A.M.  1891.  The  dec- 
lination of  the  sun  and  the  equation  of  time  will,  for 
instance,  be  the  same  on  these  two  dates. 

TABLE  44  C  gives  the  gain  of  sidereal  over  mean 
solar  time. 


No.  50.]  ASTRONOMICAL  TABLES,  ETC.  793 

TABLE  44  D  gives  the  sidereal  time  at  Greenwich 
mean  noon  for  the  10th,  20th,  and  last  day  of  every 
month  of  the  year  1891. 

TABLE  44  E  gives  the  semidiameter  of  the  sun  at 
different  times  in  the  year. 

TABLE  44  F  gives  the  declination  of  the  sun  at 
Greenwich  mean  noon  for  the  year  1891.  The  sign 
of  the  declination  is  to  be  found  at  the  head  of  the 
several  columns  (+  north,  —  south). 

TABLE  44  G  gives  the  "  equation  of  time "  at 
Greenwich  mean  noon  for  the  year  1891.  The  signs 
+  and  —  at  the  head  of  the  columns  and  elsewhere 
show  whether  the  sun  is  "fast"  or  "'slow"  respect- 
ively ;  +  indicates  that  the  sun  passes  the  meridian 
before  noon; — after  noon. 

TABLE  44  H  gives  certain  astronomical  data  relat- 
ing to  the  solar  system. 

TABLE  45  gives  the  Right  Ascension  and  Declina- 
tion of  some  of  the  most  important  stars. 

TABLE  46  gives  latitudes,  longitudes,  and  eleva- 
tions of  certain  important  places. 

TABLES  47  and  48  give  respectively  the  acceleration 
of  gravity  and  the  length  of  the  seconds  pendulum 
corresponding  to  different  latitudes.  Example  :  since 
the  latitude  of  the  Jefferson  Physical  Laboratory  of 
Harvard  College  is  42°22|'  or  42°.38,  the  acceleration 
of  gravity  is  980.37  cm.  per  sec.  per  sec. 

TABLE  49  A  and  49  B  relate  to  the  reduction  of 
measures  to  and  from  the  c.  G.  s.  system. 

TABLE  50  contains  mathematical  and  physical  con- 
stants in  frequent  use. 

14 


SOURCES   OF   AUTHORITY. 

TABLES  1-3  H  were  prepared,  in  so  far  as  possible, 
from  existing  tables,  by  rejecting  decimal  places  when 
necessary.  More  than  3,000  values  (including  all 
doubtful  cases)  were  confirmed  or  determined  by  an 
independent  calculation.  The  results  were  printed 
with  the  ordinary  precautions  to  avoid  typographical 
errors.  Tables  4-5  A  were  obtained  by  transposing 
Pickering's  tables  6-9. 

The  logarithms  of  numbers  from  1,000  to  10,000, 
in  Table  6,  were  printed  directly  from  a  copy  of  the 
tables  arranged  by  Mr.  Oliver  Whipple  Huntington, 
of  Harvard  College.  The  proofs  were  compared 
with  Bowditch's  5-place  tables  (Government  Printing- 
office,  Washington,  1882).  The  logarithms  of  num- 
bers from  10,000  to  11,000  were  obtained  by  rejecting 
figures  in  Chamber's  7-8-place  tables.  A  special  in- 
vestigation was  made  in  cases  where  the  rejected 
figures  were  50  or  500.  Stereotype-proofs  of  all  the 
logarithms  were  compared  with  the  tables  of  Gauss. 
The  table  of  probabilities  as  far  as  5.0  is  due  to 
Chauvenet.  The  remainder  of  the  table  was  the 
result  of  special  calculation. 


SOURCES  OF  AUTHORITY.  795 

The  physical  tables  (Nos.  8  to  50)  were  compiled 
for  the  most  part  by  the  aid  of  results  contained  in 
Landolt  and  Bornstein's  "Physico-Chemical  Tables,"1 
to  which  the  reader  is  referred  for  a  full  exposition  of 
the  evidence  upon  which  the  selection  of  values  has 
been  made.  The  author  wishes  to  thank  Professors 
Landolt  and  Bornstein  for  looking  over  his  manu- 
script, for  several  useful  suggestions,  and  for  their 
kind  permission  to  utilize  their  results. 

The  author  has  quoted  numerous  data  from  Ever- 
ett's "  Units  and  Physical  Constants  "  (Macmillan, 
1886).  He  has  also  made  use  of  information  given  by 
Professor  Everett  in  choosing  the  unusually  low  value 
(4.17  X  107)  for  the  mechanical  equivalent  of  heat. 

Among  other  books  from  which  results  have  been 
taken  are  the  following  :  Cooke's  Chemical  Philos- 
ophy, Deschanel's  Natural  Philosophy,  Ganot's  Phy- 
sics, Hoffmann's  Tabellen  fiir  Chemiker,  Kohlrausch's 
Leitfaden  der  Praktischen  Physik,  das  Nautisches 
Jahrbuch,  1891,  Pickering's  Physical  Manipulation, 
Stewart  and  Gee's  Practical  Physics,  Storer's  Dic- 
tionary of  Solubilities,  Trowbridge's  New  Physics, 
and  Weisbach's  Mechanics. 

These  and  other  sources  of  authority  have  been 
acknowledged  in  connection  with  the  explanation  of 
the  tables  above  ,  but  it  was  found  impossible,  in  the 
limited  space  which  could  be  devoted  to  the  tables, 
to  give  authority  for  the  separate  data.  It  was, 

1  Physikahsch-Chemische  Tabellen  von  Dr  H.  Landolt  und  Dr. 
Richard  Bornstein,  Professoren.  Verlag  von  Julius  Springer,  Montbi- 
jou  Platz  3,  Berlin. 


796  SOURCES  OF  AUTHORITY. 

moreover,  considered  inexpedient  to  present  to  stu- 
dents, who  would  naturally  be  unaccustomed  to 
weighing  evidence,  the  conflicting  statements  from 
which  the  probable  values  of  many  of  the  physical 
constants  have  to  be  estimated  by  scientific  men. 

Care  has  been  taken,  in  all  such  cases,  to  give  re- 
sults intermediate  between  those  obtained  by  different 
observers.  To  do  this,  a  considerable  number  of 
figures  was  sometimes  required ;  but  the  use  of  fig- 
ures, not  really  significant,  has  been  in  so  far  as  pos- 
sible avoided.  The  last  figure  quoted  in  the  results 
is  in  general  the  only  one  in  regard  to  which  a  differ- 
ence of  opinion  was  found  to  exist. 

It  is  regretted  that,  owing  to  the  necessity  of 
entrusting  the  composition  to  foreign  printers,  obvi- 
ous imperfections  of  type  will  be  found,  especially  in 
the  mathematical  tables.  In  the  expectation  of  re- 
printing these  tables  at  no  distant  date,  corrections 
and  suggestions  will  be  most  gladly  received. 


Table  i.  Proportional  Parts.  797 


iflV 

0 

0 

0  0 

•»•*  «*-» 
0  0 

0  0 

4*»  4CT 

0  0 

«/ur 

50 

5  10 

15 

20  25 

30  35 

4045 

1 

0 

0  0 

0  1 

1  1 

1  1 

51 

5  10 

15 

20  26 

31  36 

41  46 

2 

0 

0  1 

1  1 

1  1 

2  2 

52 

5  10 

16 

21  26 

31  36 

42  47 

3 

0 

1  1 

1  2 

2  2 

2  3 

53 

5  11 

16 

21  27 

32  37 

42  48 

4 

0 

1  1 

2  2 

2  3 

3  4 

54 

5  11 

16 

22  27 

32  38 

43  49 

5 

1  2 

2  3 

3  4 

4  5 

55 

6  11 

17 

22  28 

33  39 

44  50 

6 

1  2 

2  3 

4  4 

5  5 

56 

6  11 

17 

22  28 

34  39 

45  50 

7 

1  2 

3  4 

4  5 

6  6 

57 

6  11 

17 

23  29 

34  40 

46  51 

8 

2  2 

3  4 

5  6 

6  7 

58 

6  12 

17 

23  29 

35  41 

46  52 

9 

2  3 

4  5 

5  6 

7  8 

59 

6  12 

18 

24  30 

35  41 

47  53 

10 

2  3 

4  5 

6  7 

8  9 

60 

6  12 

18 

24  30 

36  42 

48  54 

11 

2  3 

4  6 

7  8 

9  10 

61 

6  12 

18 

24  31 

37  43 

49  55 

12 

2  4 

5  6 

7  8 

10  11 

62 

6  12 

19 

25  31 

37  43 

50  56 

13 

3  4 

5  7 

8  9 

10  12 

63 

6  13 

19 

25  32 

38  44 

50  57 

14 

3  4 

6  7 

8  10 

11  13 

64 

6  13 

19 

26  32 

38  45 

51  58 

15 

2 

3  5 

6  8 

9  11 

12  14 

65 

7  13 

20 

26  33 

39  46 

52  59 

16 

2 

3  5 

6  8 

10  11 

13  14 

66 

7  13 

20 

26  33 

40  46 

53  59 

17 

2 

3  5 

7  9 

10  12 

14  15 

67 

7  13 

20 

27  34 

40  47 

54  60 

18 

2 

4  5 

7  9 

11  13 

14  16 

68 

7  14 

20 

27  34 

41  48 

54  61 

19 

2 

4  6 

8  10 

11  13 

15  17 

69 

7  14 

21 

28  35 

41  48 

55  62 

20 

2 

4  6 

8  10 

12  14 

16  18 

70 

7  14 

21 

28  35 

42  49 

56  63 

21 

2 

4  6 

8  11 

13  15 

17  19 

71 

7  14 

21 

28  36 

43  50 

57  64 

22 

2 

4  7 

9  11 

13  15 

18  20 

72 

7  14 

22 

29  36 

43  50 

58  65 

23 

2 

5  7 

9  12 

14  16 

18  21 

73 

7  15 

22 

29  37 

44  51 

58  66 

24 

2 

5  7 

10  12 

14  17 

19  22 

74 

7  15 

22 

30  37 

44  52 

59  67 

25 

3 

5  8 

10  13 

15  18 

20  23 

75 

8  15 

23 

30  38 

45  53 

60  68 

26 

3 

5  8 

10  13 

16  18 

21  23 

76 

8  15 

23 

30  38 

46  53 

61  68 

27 

3 

5  8 

11  14 

16  19 

22  24 

77 

8  15 

23 

31  39 

46  54 

62  69 

28 

3 

6  8 

11  14 

17  20 

22  25 

78 

8  16 

23 

31  39 

47  55 

62  70 

29 

3 

6  9 

12  15 

17  20 

23  26 

79 

8  16 

24 

32  40 

47  55 

63  71 

30 

3 

6  9 

12  15 

18  21 

24  27 

80 

8  16 

24 

32  40 

48  56 

64  72 

31 

3 

6  9 

12  16 

19  22 

25  28 

81 

8  16 

24 

32  41 

49  57 

65  73 

32 

3 

6  10 

13  16 

19  22 

26  29 

82 

8  16 

25 

33  41 

49  57 

66  74 

33 

^ 

7  10 

13  17 

20  23 

26  30 

83 

8  17 

25 

33  42 

50  58 

66  75 

34 

3 

7  10 

14  17 

20  24 

27  31 

84 

8  17 

25 

34  42 

50  59 

67  76 

35 

4 

7  11 

14  18 

21  25 

28  32 

85 

9  17 

26 

34  43 

51  60 

68  77 

36 

4 

7  11 

14  18 

22  25 

29  32 

86 

9  17 

26 

34  43 

52  60 

69  77 

37 

4 

7  11 

15  19 

22  26 

30  33 

87 

9  17 

26 

35  44 

52  61 

70  78 

38 

4 

8  11 

15  19 

23  27 

30  34 

88 

9  18 

26 

35  44 

53  62 

70  79 

39 

4 

8  12 

16  20 

23  27 

31  35 

89 

9  18 

27 

36  45 

53  62 

71  80 

40 

4 

8  12 

16  20 

24  28 

32  36 

90 

9  18 

27 

36  45 

54  63 

72  81 

41 

4 

8  12 

16  21 

25  29 

33  37 

91 

9  18 

27 

36  46 

55  64 

73  82 

42 

4 

8  13 

17  21 

25  29 

34  38 

92 

9  18 

28 

37  46 

55  64 

74  83 

43 

4 

9  13 

17  22 

26  30 

34  39 

93 

9  19 

28 

37  47 

56  65 

74  84 

44 

4 

9  13 

18  22 

26  31 

35  40 

94 

9  19 

28 

38  47 

56  66 

75  85 

45 

5 

9  14 

18  23 

27  32 

36  41 

95 

10  19 

29 

38  48 

57  67 

76  86 

46 

5 

9  14 

18  23 

28  32 

37  41 

96 

10  19 

29 

38  48 

58  67 

77  86 

47 

5 

9  14 

19  24 

28  33 

38  42 

97 

10  19 

29 

39  49 

58  68 

78  87 

48 

5 

10  14 

19  24 

29  34 

38  43 

98 

10  20 

29 

39  49 

59  69 

78  88 

49 

5 

10  15 

20  25 

29  34 

39  44 

99 

10  20 

30 

40  50 

59  69 

79  89 

50 

5 

10  15 

20  25 

30  35 

40  45 

100 

10  20 

30 

40  50 

60  70 

80  90 

798 


Powers. 


Table  2. 


so.  a-fRnercar'-£re  <•*»'•  *•**• 


.r.,        a.  Recip-      6.  Square       -  ,   p. 

flO,          rocaj  Root      c.  Square         4.  Cubi 


0 

CO 

0.00 

0 

0 

50 

.0200 

7.07 

2500 

125000 

1 

1.000 

1.00 

1 

1 

51 

196 

7.14 

2601 

132651 

2 

0.500 

1.41 

4 

8 

52 

192 

7.21 

2704 

140608 

3 

333 

1.73 

9 

27 

53 

189 

7.2S 

2809 

148877 

4 

250 

2.00 

16 

64 

54 

185 

7.35 

2916 

157464 

5 

0.200 

2.24 

25 

125 

55 

.0182 

7.42 

3025 

166375 

6 

167 

2.45 

36 

216 

56 

179 

7.48 

3136 

175616 

7 

143 

2.65 

49 

343 

57 

175 

7.55 

3249 

185193 

8 

125 

2.83 

64 

512 

58 

172 

7.62 

3364 

195112 

9 

111 

3.00 

81 

729 

59 

169 

7.68 

3481 

205379 

10 

0.100 

3.16 

100 

1000 

60 

.0167 

7.75 

3600 

21COOO 

11 

.0909 

3.32 

121 

1331 

61 

164 

7.81 

3721 

220981 

12 

833 

346 

144 

1728 

62 

161 

7.87 

3844 

238328 

13 

769 

3.61 

169 

2197 

63 

159 

7.94 

3969 

250047 

14 

714 

3.74 

196 

2744 

64 

156 

8.00 

4096 

262144 

15 

.0607 

3.87 

225 

3375 

65 

.0154 

8.06 

4225 

274625 

16 

625 

4.00 

256 

4096 

66 

152 

8.12 

4356 

287496 

17 

588 

4.12 

289 

4913 

67 

149 

8.19 

4489 

300763 

18 

556 

4.24 

324 

5832 

68 

147 

8.25 

4624 

314432 

19 

526 

4.36 

361 

6859 

69 

145 

8.31 

4761 

328509 

20 

.0500 

4.47 

400 

8000 

70 

.0143 

8.37 

4900 

343000 

21 

476 

4.58 

441 

9261 

71 

141 

8.43 

5041 

357911 

22 

455 

4.69 

484 

10648 

72 

139 

8.49 

5184 

373248 

23 

435 

4.80 

529 

12167 

73 

137 

8.54 

5329 

389017 

24 

417 

4.90 

576 

13824 

74 

135 

860 

5476 

405224 

25 

.0400 

5.00 

625 

15625 

75 

0133 

8.66 

5625 

421875 

26 

385 

5.10 

676 

17576 

76 

132 

8.72 

5776 

438976 

27 

370 

5.20 

729 

19683 

77 

130 

8.77 

5929 

456533 

28 

357 

5.29 

784 

21952 

78 

128 

883 

6084 

474552 

29 

345 

5.39 

841 

24389 

79 

127 

8.89 

6241 

493039 

30 

.0333 

5.48 

900 

27000 

80 

.0125 

8.94 

6400 

512000 

31 

323 

5.57 

961 

29791 

81 

123 

9.00 

6561 

531441 

32 

313 

5.66 

1024 

32768 

82 

122 

9.06 

6724 

551368 

33 

303 

5.74 

1089 

35937 

83 

120 

9.11 

6889 

571787 

34 

294 

5.83 

1156 

39304 

84 

119 

9.17 

7056 

592704 

35 

.0286 

5.92 

1225 

42875 

85 

.0118 

9.22 

7225 

614125 

36 

278 

6.00 

1296 

40656 

86 

116 

9.27 

7396 

63.6056 

37 

270 

6.08 

1369 

50653 

87 

115 

9.33 

7569 

658503 

38 

263 

6.16 

1444 

54872 

88 

114 

9.38 

7744 

681472 

39 

256 

6.24 

1521 

59319 

89 

112 

9.43 

7921 

704969 

40 

.0250 

6.32 

1600 

64000 

90 

.0111 

9.49 

8100 

729000 

41 

244 

640 

1681 

68921 

91 

110 

9.54 

8281 

753571 

42 

238 

6.48 

1764 

74088 

92 

109 

9.59 

8464 

778688 

43 

233 

6.56 

1849 

79507 

93 

m 

9.64 

8649 

804357 

44 

227 

6.63 

1936 

85184 

94 

106 

9.70 

8836 

830584 

45 

.0222 

6.71 

2025 

91125 

95 

.0105 

9.75 

9025 

857375 

46 

217 

6.78 

2116 

97336 

96 

104 

9.80 

9216 

884736 

47 

213 

6.86 

2209 

103823 

97 

103 

9.85 

9409 

912673 

48 

208 

6.93 

2304 

110592 

98 

102 

9.90 

9604 

941192 

49 

204 

7.00 

2401 

117649 

99 

101 

9.95 

9301 

970299 

50 

.0200 

7.07 

2500 

125000 

100 

.0100 

10.00 

10000 

1000000 

Table  2. 


Circles,  etc. 


799 


Diam- 
eter 

..Log- 
arithm 

/.  Circum- 
ference 

g.  Area 
of  Circle 

h.  Volume 
of  Sphere 

Diam- 
eter 

e.  Log- 
arithm 

f.  Ciroum- 

ference 

g.  Area  h. 
of  Circle  of 

Volume 
Sphere 

.0 

—CO 

0.00 

0.00 

.000 

5.0 

0.699 

15.71 

19.6 

65 

.1 

rooo 

31 

01 

.001 

5.1 

708 

16.02 

20.4 

69 

.2 

301 

63 

03 

.004 

5.2 

716 

16.34 

21.2 

74 

.3 

477 

94 

07 

.014 

5.3 

724 

16.65 

22.1 

78 

.4 

602 

1.26 

13 

.034 

5.4 

732 

16.96 

22.9 

82 

.5 

T.699 

1-57 

0.20 

.065 

5.5 

0.740 

17.28 

23.8 

87 

.6 

778 

1.88 

28 

.113 

5.6 

748 

17.59 

24.6 

92 

.7 

845 

2.20 

38 

.180 

5.7 

756 

17.91 

25.5 

97 

.8 

903 

2.51 

50 

.268 

5.8 

763 

18.22 

26.4 

102 

.9 

954 

2.83 

64 

.382 

5.9 

771 

18.54 

27.3 

108 

1.0 

0.000 

3.14 

0.79 

0.52 

6.0 

0.778 

18.85 

28.3 

113 

M 

041 

3.46 

0.95 

70 

6.1 

785 

19.16 

29,2 

119 

1.2 

079 

3.77 

1.13 

90 

6.2 

792 

19.48 

30.2 

125 

1.3 

114 

4.08 

1.33 

1.15 

6.3 

799 

19.79 

31.2 

131 

1.4 

146 

4.40 

1.54 

1.44 

6.4 

806 

20.11 

32.2 

137 

1.5 

0.176 

4.71 

1.77 

1.77 

6.5 

0.813 

20.42 

33.2 

144 

1.6 

204 

5.03 

2.01 

2.14 

6.6 

820 

20.73 

34.2 

151 

1.7 

230 

5.34 

2.27 

2.57 

6.7 

826 

21.05 

35.3 

157 

1.8 

255 

5.65 

2.54 

3.05 

6.8 

833 

21.36 

36.3 

165 

1.9 

279 

5.97 

2.81 

3.59 

6.9 

839 

21.68 

37.4 

172 

2.0 

0.301 

6.28 

3.14 

4.19 

7.0 

0.845 

21.99 

38.5 

180 

2.1 

322 

6.60 

3.46 

4.85 

7.1 

851 

22.31 

39.6 

187 

2.2 

342 

6.91 

3.80 

5.58 

7.2 

857 

22.62 

40.7 

195 

2.3 

362 

7.23 

4.15 

6.37 

73 

863 

22.93 

41.9 

204 

2.4 

380 

7.54 

4.52 

7.24 

7.4 

869 

23.25 

43.0 

212 

2.5 

0.398 

7.85 

4.91 

8.2 

7.5 

0.875 

23.56 

44.2 

221 

2.6 

415 

8.17 

5.31 

9.2 

7.6 

881 

23.88 

45.4 

230 

2.7 

431 

8.48 

5.73 

10.3 

7.7 

886 

24.19 

46.6 

239 

2.8 

447 

8.80 

6.16 

11.5 

7.8 

892 

24.50 

47.8 

248 

2.9 

462 

9.11 

661 

12.8 

7.9 

898 

2482 

49.0 

258 

3.0 

0.477 

9.42 

7.C7 

14.1 

8.0 

0.903 

25.13 

50.3 

268 

3.1 

491 

9.74 

7.55 

15.6 

81 

908 

25.45 

51.5 

278 

3.2 

505 

10.05 

8.04 

17.2 

8.2 

914 

25.76 

52.8 

289 

3.3 

519 

10.37 

8,55 

18.8 

8.3 

919 

26.08 

541 

299 

3.4 

531 

10.68 

9.08 

20.6 

8.4 

924 

2639 

55.4 

310 

3.5 

0.544 

11.00 

9.6 

22.4 

8.5 

0.929 

26.70 

56.7 

322 

3.6 

556 

11.31 

102 

24.4 

8.6 

934 

27.02 

58.1 

333 

3.7 

568 

11.62 

10.8 

26.5 

8.7 

940 

27,33 

59.4 

345 

3.8 

580 

11.94 

11.3 

28.7 

8.8 

944 

27.65 

60.8 

357 

3.9 

591 

12.25 

11.9 

31.1 

8.9 

949 

27.96 

62.2 

369 

4.0 

0.602 

12.57 

12.6 

33.5 

9.0 

0.954 

28.27 

63.6 

382 

4.1 

613 

12.88 

13.2 

36.1 

9.1 

959 

28.59 

65.0 

395 

4.2 

623 

13.19 

13.9 

38.8 

9.2 

964 

28.90 

66.5 

408 

4.3 

633 

13.51' 

14.5 

41.6 

9.3 

968 

29.22 

67.9 

421 

4.4 

643 

13.82 

15.2 

44.6 

9.4 

973 

29.53 

69.4 

435 

4.5 

0.653 

14.14 

15.9 

47.7 

9.5 

0.978 

29.85 

70.9 

449 

4.6 

663 

14.45 

16.6 

51.0 

9.6 

982 

30.16 

72.4 

463 

4.7 

672 

14.77 

173 

54.4 

9.7 

987 

30.47 

73.9 

478 

4.8 

681 

15.08 

18.1 

57.9 

9.8 

991 

30.79 

75.4 

493 

4.9 

690 

15.39 

18.9 

61.6 

99 

996 

31.10 

77.0 

508 

5.0 

0.699 

15.71 

19.6 

65.4 

10.0 

1.000 

31.42 

78.5 

524 

800  Trigonometric  Functions.  Tables. 

o.  Angle.  6.  Tangent,     e.  Arc.       d.  Chord,      e.  Sim.      /".Cosine.       g.  Rate  of       h.  Secant,    i.  Compli- 

Vibration.  oient. 


0° 

0.000 

0.000 

0.000 

0.000 

1.000 

1.00000 

1.000 

90° 

1 

017 

017 

017 

017 

1.000 

1.00000 

1,000 

89 

2 

035 

035 

035 

035 

0.999 

0.99998 

1.001 

88 

3 

052 

052 

052 

052 

999 

99996 

1.001 

87 

4 

070 

070 

070 

070 

998 

99992 

1.002 

86 

5 

0.087 

0.087 

0.087 

0.087 

0.996 

0.99988 

1.004 

85 

6 

105 

105 

105 

105 

995 

99983 

1.006 

84 

7 

123 

122 

122 

122 

993 

99977 

1.008 

83 

8 

141 

140 

140 

139 

990 

99970 

1.010 

82 

9 

158 

157 

157 

156 

988 

99961 

L012 

81 

10 

0.176 

0.175 

0.174 

0.174 

0.985 

0.99952 

1.015 

80 

11 

194 

192 

192 

191 

982 

99942 

1.019 

79 

12 

213 

209 

209 

208 

978 

99931 

1.022 

78 

13 

231 

227 

226 

225 

974 

99920 

1.026 

77 

14 

249 

244 

244 

242 

970 

99907 

1.031 

76 

15 

0.268 

0.262 

0.261 

0.259 

0.966 

0.99893 

1.035 

75 

16 

287 

279 

278 

3,76 

961 

99878 

1.040 

74 

17 

306 

297 

296 

292 

956 

99862 

1.046 

73 

18 

325 

314 

313 

309 

951 

99846 

1.051 

72 

19 

344 

332 

330 

326 

946 

99828 

1.058 

71 

20 

0.364 

0.349 

0.347 

0.342 

0.940 

0.99810 

1.064 

70 

21 

384 

367 

364 

35JS 

954 

99790 

1.071 

69 

22 

404 

384 

382 

3/5 

927 

99770 

1-079 

68 

2S 

424 

401 

399 

391 

921 

99749 

1.086 

67 

24 

445 

419 

416 

407 

914 

99726 

1.095 

66 

25 

0.466 

0.436 

0.433 

0.423 

0.906 

0.99703 

1.103 

65 

26 

488 

454 

450 

438 

899 

99678 

1.113 

64 

27 

no 

471 

467 

454 

891 

99653 

1.122 

63 

28 

532 

489 

484 

469 

883 

99627 

1.133 

62 

29 

554 

506 

501 

485 

875 

99600 

1.143 

61 

30 

0.577 

0.524 

0.518 

0.500 

0.866 

0.99572 

1.155 

60 

31 

601 

541 

534 

515 

857 

99543 

1.167 

59 

32 

625 

559 

551 

530 

848 

99513 

1.179 

58 

33 

649 

576 

568 

545 

839 

99482 

1.192 

57 

34 

675 

593 

585 

559 

829 

99450 

1.206 

56 

35 

0.700 

0.611 

0.601 

0.574 

0.819 

0.99417 

1.221 

55 

36 

727 

628 

618 

588 

809 

99384 

1.236 

54 

37 

754 

646 

635 

602 

799 

99349 

1.252 

53 

38 

781 

663 

651 

616 

788 

99314 

1.269 

52 

39 

810 

681 

668 

629 

777 

99277 

1.287 

51 

40 

0.839 

0.698 

0.684 

0.643 

0.766 

0.99239 

1.305 

50 

41 

869 

716 

700 

656 

755 

99200 

1.325 

49 

42 

900 

733 

717 

669 

743 

99161 

1.346 

48 

43 

933 

750 

733 

682 

731 

99121 

1.367 

47 

44 

966 

768 

749 

695 

719 

99079 

1,390 

46 

45° 

1.000 

0.785 

0.765 

0.707 

0.707 

0,99037 

1.414 

45* 

fable  3. 


Trigonometric  Functions. 


801 


a.  Angli. 

6.  Tangent. 

t.  Are. 

d.  Chord. 

e.  Sill. 

f.  Cosini. 

g.  Coversini 

h.  Secant. 

».  Compli- 

ment. 

45° 

1.000 

0.785 

0.765 

0.707 

0.707 

0.293 

1.414 

45» 

46 

1.036 

0.803 

781 

719 

695 

281 

1.440 

44 

47 

1.072 

0,820 

797 

731 

682 

269 

1.466 

43 

48 

1.111 

0.838 

813 

743 

669 

257 

1.494 

42 

49 

1.150 

0.855 

829 

755 

656 

245 

1.524 

41 

50 

1.192 

0.873 

0.845 

0.766 

0.643 

0.234 

1.556 

40 

51 

1.235 

0.890 

861 

777 

629 

223 

1.589 

39 

52 

1.280 

0.908 

877 

788 

616 

212 

1.624 

38 

53 

1.327 

0,925 

892 

799 

602 

201 

1.662 

37 

54 

1.376 

0.942 

908 

809 

588 

191 

1.701 

36 

55 

1.428 

0.960 

0.923 

0.819 

0.574 

0.181 

1.743 

35 

56 

1.483 

0.977 

939 

829 

559 

171 

1.788 

34 

57 

1.540 

0,995 

954 

839 

545 

161 

1.836 

33 

58 

1.600 

1.012 

970 

848 

530 

152 

1.887 

32 

59 

1.664 

1.030 

985 

857 

515 

143 

1942 

31 

60 

1.732 

1.047 

1.000 

0.866 

0.500 

0.134 

2.000 

30 

61 

1.804 

1.065 

1.015 

875 

485 

125 

2.003 

29 

62 

1.881 

1.082 

1.030 

883 

469 

117 

2.130 

28 

63 

1.963 

1.100 

1.045 

891 

454 

109 

2.203 

27 

64 

2.050 

1.117 

1.060 

899 

438 

101 

2.281 

26 

65 

2.145 

1.134 

1.075 

0.906 

0.423 

0.094 

2.366 

25 

66 

2.246 

1.152 

1.089 

914 

407 

086 

2.459 

24 

67 

2.356 

1.169 

1.104 

921 

391 

079 

2-559 

23 

68 

2.475 

1.187 

1.118 

927 

375 

073 

2.669 

22 

69 

2.605 

1.204 

1.133 

934 

358 

066 

2.790 

21 

70 

2.747 

1.222 

1.147 

0.940 

0.342 

0.060 

2.924 

20 

71 

2.904 

1.239 

1.161 

946 

326 

054 

3.072 

19 

72 

3.078 

1.257 

1.176 

951 

309 

049 

3.236 

18 

73 

3.271 

1.274 

1.190 

956 

292 

044 

3.420 

17 

74 

3.487 

1.292 

1.204 

961 

276 

039 

3.628 

16 

75 

3.732 

1.309 

1218 

0.966 

0.259 

0.034 

3.864 

15 

76 

4.011 

1.326 

1.231 

970 

242 

030 

4.134 

14 

77 

4.331 

1.344 

1.245 

974 

225 

026 

4.445 

13 

78 

4,705 

1.361 

1.259 

978 

208 

022 

4.810 

12 

79 

5.145 

1.379 

1.272 

982 

191 

01S 

5.241 

11 

80 

5.671 

1.396 

1.286 

0985 

0.174 

0.0152 

5.759 

10 

81 

6.314 

1414 

1299 

988 

156 

0123 

6.392 

9 

82 

7.115 

1.431 

1.312 

990 

139 

0097 

7.185 

8 

83 

8.144 

1.449 

1.325 

993 

122 

0075 

8.206 

7 

84 

9.514 

1.466 

1.338 

995 

105 

0055 

9.567 

6 

85 

11.43 

1.484 

1.351 

0.996 

0.087 

0.00381 

11.47 

5 

86 

14.30 

1.501 

1364 

998 

070 

00244 

14.34 

4 

87 

19.08 

1.518 

1.377 

999 

052 

00137 

19.11 

3 

88 

28.64 

1.536 

1.389 

999 

035 

00061 

28.65 

2 

89 

57.29 

1.553 

1402 

1.000 

017 

00015 

57.30 

1 

90° 

00 

1.571 

1.414 

1.000 

0.000 

0.00000 

00 

802  Reciprocals.  Table  3,  A. 

M  0          128456789       Bit. 

1.0  1.0000  9901  9804  9709  9615  9524  9434  9346  9259  9174  » 

1.1  0.9091  9009  8929  8850  8772  8696  8621  8547  8475  8403  76 

1.2  8333  8264  8197  8130  8065  8000  7937  7874  7813  7752  6b 

1.3  7692  7634  7576  7519  7463  7407  7353  7299  7246  7194  » 

1.4  7143  7092  7042  6993  6944  6897  6849  6803  6757  6711  • 

1.5  0.6667  6623  6579  6536  6494-  6452  6410  6369  6329  6289  " 

1.6  6250  6211  6173  6135  6098  6061  6024  5988  5952  5917  « 

1.7  5882  5848  5814  5780  5747  5714  5682  5650  5618  5587  » 

1.8  5556  5525  5495  5464  5435  5405  5376  5348  5319  5291  » 

1.9  5263  5236  5208  5181  5155  5128  5102  5076  5051  5025  » 

2.0  0.5000  4975  4950  4926  4902  4878  4854  4831  4808  4785  " 

2.1  4762  4739  4717  4695  4673  4651  4630  4608  4587  4566  " 

2.2  4545  4525  4505  4484  4464  4444  4425  4405  4386  4367  80 

2.3  4348  4329  4310  4292  4274  4255  4237  4219  4202  4184  18 

2.4  4167  4149  4132  4115  4098  4082  4065  4049  4032  4016  1T 

2.5  0.4000  3984  3968  3953  3937  3922  3906  3891  3876  3861  w 

2.6  3846  3831  3817  3802  3788  3774  3759  3745  3731  3717  " 

2.7  3704  3690  3676  3663  3650  3636  3623  3610  3597  3584  13 

2.8  8571  3559  3546  3534  3521  3509  3496  3484  3472  3460  " 

2.9  3448  3436  3425  3413  3401  3390  3378  3367  3356  3344  » 

3.0  0.3333  3322  3311  3300  3289  3279  3268  3257  3247  3236  " 

3.1  3226  3215  3205  3195  3185  3175  3165  3155  3145  3135  » 

3.2  3125  3115  3106  3096  3086  3077  3067  3058  3049  3040   * 

3.3  3030  3021  3012  3003  2994  2985  2976  2967  2959  2950   • 

3.4  2941  2933  2924  2915  2907  2899  2890  2882  2874  2865 

3.5  0.2857  2849  2841  2833  2825  2817  2809  2801  2793  2786   8 

3.6  2778  2770  2762  2755  2747  2740  2732  2725  2717  2710 

3.7  2703  2695  2688  2681  2674  2667  2660  2653  2646  2639   7 

3.8  2632  2625  2618  2611  2604  2597  2591  2584  2577  2571 

3.9  2564  2558  2551  2545  2538  2532  2525  2519  2513  2506 

4.0  0.2500  2494  2488  2481  2475  2469  2463  2457  2451  2445   6 

4.1  2439  2433  2427  2421  2415  2410  2404  2398  2392  2387 

4.2  2381  2375  2370  2364  2358  2353  2347  2342  2336  2331 

4.3  2326  2320  2315  2309  2304  2299  2294  2288  2283  2278 

4.4  2273  2268  2262  2257  2252  2247  2242  2237  2232  2227   * 

4.5  0.2222  2217  2212  2208  2203  2198  2193  2188  2183  2179 

4.6  2174  2169  2165  2160  2155  2151  2146  2141  2137  2132 

4.7  2128  2123  2119  2114  2110  2105  2101  2096  2092  2088 

4.8  2083  2079  2075  2070  2066  2062  2058  2053  2049  2045 
4.Q  2041  2037  2033  2028  2024  2020  2016  2012  2008  2004 

5.0  0.2000  1996  1992  1988  1984  1980  1976  1972  1969  1965  * 

5.1  1961  1957  1953  1949  1946  1942  1638  1934  1931  1927 

5.2  1923  1919  1916  1912  1908  1905  1901  1898  1894  1890 

5.3  1887  1883  1880  1876  1873  1869  1866  1862  1859  1855 

5.4  1852  1848  1845  1842  1838  1835  1832  1828  1825  1821 

5.5  0.1818  1815  1812  1808  1805  1802  1799  1795  1792  1789 

5.6  1786  1783  1779  1776  1773  1770  1767  1764  1761  1757 

5.7  1754  1751  1748  1745  1742  1739  1736  1733  1730  1727   • 

5.8  1724  1721  1718  1715  1712  1709  1706  1704  1701  1698 

5.9  1695  1692  1689  1686  1684  1681  1678  1C75  1672  1669 
<>.0  0.1667  1664  1661  1658  1656  1653  1650  1647  1645  1642 


Table  s,  A.  Reciprocals.  803 

M          0123456789    •«• 

6.0  0.16667  16639  16611  16584  16556  16529  16502  16474  16447  16420  27 

6.1  16393  16367  16340  16313  16287  16260  16234  16207  16181  16155  26 

6.2  16129  16103  16077  16051  16026  16000  15974  15949  15924  15898  8e 

6.3  15873  15848  15823  15798  15773  15748  15723  15699  15674  15649  25 

6.4  15625  15601  15576  15552  15528  15504  15480  15456  15432  15408  24 

6.5  0.15385  J5361  15337  15314  15291  15267  15244  15221  15198  15175  23 

6.6  15152  15129  15106  15083  15060  15038  15015  14992  14970  14948  23 

6.7  14925  14903  14881  14859  14837  14815  14793  14771  14749  14728  22 

6.8  14706  14684  14663  14641  14620  14599  14577  14556  14535  14514  21 

6.9  14493  14472  14451  14430  14409  14388  14368  14347  14327  14306  21 

7.0  0.14286  14265  14245  14225  14205  14184  14164  14144  14124  14104  20 

7.1  14085  14065  14045  14025  14006  13986  13966  13947  13928  13908 

7.2  13889  13870  13850  13831  13812  13793  13774  13755  13736  13717  19 

7.3  13699  13680  13661  13643  13624  13605  13587  13569  13550  13532 

7.4  13514  13495  13477  13459  13441  13423  13405  13387  13369  13351  18 

7.5  0.13333  13316  13298  13280  13263  13245  13228  13210  13193  13175 

7.6  13158  13141  13123  13106  13089  13072  13055  13038  13021  13004  " 

7.7  12987  12970  12953  12937  12920  12903  12887  12870  12853  12837 

7.8  12821  12804  12788  12771  12755  12739  12723  12706  12690  12674  l6 

7.9  12658  12642  12626  12610  12594  12579  12563  12547  12531  12516 

8.0  0.12500  12484  12469  12453  12438  12422  12407  12392  12376  12361 

8.1  12346  12330  12315  12300  12285  12270  12255  12240  12225  12210  I5 

8.2  12195  12180  12165  12151  12136  12121  12107  12092  12077  12063 

8.3  12048  12034  12019  12005  11990  11976  11962  11947  11933  11919 

8.4  11905  11891  11876  11862  11848  11834  11820  11806  11792  11779  " 

8.5  0.11765  11751  11737  11723  11710  11696  11682  11669  11655  11641 

8.6  11628  11614  11601  11587  11574  11561  11547  11534  11521  11507 

8.7  11494  11481  11468  11455  11442  11429  11416  11403  11390  11377  13 

8.8  11364  11351  11338  11325  11312  11299  11287  11274  11261  11249 

8.9  11236  11223  11211  11198  11186  11173  11161  11148  11136  11123 

900.11111  11099  11086  11074  11062  11050  11038  11025  11013  11001 

9.1  10989  10977  10965  10953  10941  10929  W917  10905  10893  10881  12 

9.2  10870  10858  10846  10834  10823  10811/10799  10787  10776  10764 

9.3  10753  10741  10730  10718  10707  10695  10684  10672  10661  10650 
94  10638  10627  10616  10604  10593  10582  10571  10560  10549  10537 

9.5  0.10526  10515  10504  10493  10482  10471  10460  10449  10438  10428  » 

9.6  10417  10406  10395  10384  10373  10363  10352  10341  10331  10320 
97  10309  10299  10288  10277  10267  10256  10246  10235  10225  10215 
9.8  10204  10194  10183  10173  10163  10152  10142  10132  10121  10111 
99  10101  10091  10081  10070  10060  10050  10040  10030  10020  10010 

10.00.10000.09990  9980  9970  9960  9950  9940  9930  9921  9911  » 

10.1  .09901  9891  9881  9872  9862  9852  9843  9833  9823  9814 

10.2  9804  9794  9785  9775  9766  9756  9747  9737  9728  9718 

10.3  9709  9699  9690  9681  9671  9662  9653  9643  9634  9625 

10.4  9615  9606  9597  9588  9579  9569  9560  9551  9542  9533 

10.50.09524  9515  9506  9497  9488  9479  9470  9461  9452  9443  • 

10.6  9434  9425  9416  9407  9398  9390  9381  9372  9363  9355 

10.7  9348  9337  9328  9320  9311  9302  9294  9285  9276  9268 

10.8  9259  9251  9242  9234  9225  9217  9208  9200  9191  9183 

10.9  9174  9166  9158  9149  9141  9132  9124  9116  9107  9099 
11.00.09091  9083  9074  9066  9058  9050  9042  9033  9025  9017  • 


804  Squares.  Table  a.  c, 

J\s       0         1         2  34  567  89     •«. 

1.0  1.000  1.020  1.040  1.061  1.082  1.103  1.124  1.145  1.166  1.188  21 

1.1  1.210  1.232  1.254  1.277  1.300  1.323  1.346  1.369  1.392  1.416  » 

1.2  1.440  1.464  1.488  1.513  1.538  1.563  1.588  1.613  1.688  1.664* 

1.3  1.690  1.716  1.742  1.769  1.796  1.823  1.850  1.877  1.904  1.932  " 

1.4  1.960  1.988  2.016  2.045  2.074  2.103  2.132  2.161  2.190  2.2*20  3S 

1.5  2.250  2.280  2.310  2.341  2.372  2.403  2-434  2.465  2.496  2.528  81 

1.6  2.560  2  592  2.624  2.657  2.690  2.723  2.756  2.789  2.822  2.856  88 
1>  2.890  2.924  2.958  2.993  3.028  3.063  3.098  3.133  3.168  3.204  * 
1.8  3.240  3.276  3.312  3.349  3.386  3.423  3.460  3.497  3.534  3.572  87 
1.0  3.610  3.64$  1686  3.725  3.764  3.803  3.842  3.881  3.920  3.960  89 

2.0  4.000  4.040  4.080  4.121  4.162  4.203  4.244  4.285  4.326  4.368  tt 

2.1  4.410  4.452  4.494  4.537  4.580  4.623  4.666  4.709  4.752  4.796  4| 

2.2  4.840  4.884  4.928  4.973  5.018  5.063  5.108  5.153  5.198  5.244  « 

2.3  5.290  5.336  5.382  5.429  5.476  5.523  5.570  5.617  5.664  5.712* 

2.4  5.760  5.808  5.856  5.905  5.954  6.003  6.052  6.101  6.150  6.200  « 

2.5  6.250  6.300  6.350  6.401  6.452  6.503  6.554  6.605  6.656  6.708  M 

2.6  6.760  6.812  6.864  6.917  6.970  7.023  7.076  7.129  7.182  7  236  63 

2.7  7.290  7.344  7.398  7.453  7.508  7.563  7.618  7.673  7.728  7.784" 

2.8  7.840  7.896  7.952  8.009  8.066  8.123  8,180  8.237  8.294  8  352  67 

2.9  8.410  8.468  8.526  8.585  8.644  8.703  8.762  8.821  8.880  8.940  69 

3.0  9.000  9.060  9.120  9.181  9.242  9.303  9.364  9.425  9.486  9.548  61 

3.1  9.610  9.672  9.734  9.797  9.860  9.923  9.986  10.05  10.11  10.18- 

3.2  10.24  10.30  10.37  10.43  10.50  10.56  10.63  10.69  10.76  10.82 

3.3  10.89  10.96  11.02  11.09  11.16  11.22  11.29  11.36  11.42  11.49 

3.4  11.56  11.63  11.70  11.76  11.83  11.90  11.97  12.04  12.11  12.18 

3.5  12.25  12.32  12.39  12.46  12.53  12.60  12.67  12.74  12.82  12.89  7 

3.6  12.96  13.03  13.10  13.18  13.25  13.32  13.40  13.47  13.54  13.62 

3.7  13.69  13.76  13.84  13.91  13.99  14.06  14.14  14.21  14.29  14.36 

3.8  14.44  14.52  14.59  14.67  1475  14.82  14.90  14.98  15.05  15.13 
3.0  15.21  15.29  15.37  15.44  15.52  15.60  15.68  15.76  15.84  15.92 

4.0  16.00  16.08  16.16  16.24  16.32  16.40  16.48  16.56  16.65  16.73    8 

4.1  16.81  16.89  16.97  17.06  17.14  17.22  17.31  17.39  17.47  17.56 

4.2  17.64  17.72  17.81  17,89  17.98  18.06  18.15  18.23  18.32  18.40 

4.3  18.49  18.58  18.66  18.75  18.84  18.92  19.01  19.10  19.18  19.27 

4.4  19.36  19.45  19.54  19.62  19.71  19.80  19.89  19.98  20.07  20.16 

4.5  20.25  20.34  20.43  20.52  20.61  20.70  20.79  20.88  20.98  21.07    9 

4.6  21.16  21.25  21.34  21.44  21.53  21.62  21.72  21.81  21.90  22.00 

4.7  22.09  22.18  22.28  2237  22.47  22.56  22.66  22.75  22.85  22.94 

4.8  23.04  23.14  23.23  23.33  23.43  23.52  23.62  23.72  23.81  23.91 

4.9  24.01  24.11  24.21  24.30  2440  24.50  24.60  24.70  24.80  24.90 

5.0  25.00  25.JO  25.20  25.30  25.40  25.50  25.60  25.70  25.81  25.91  *> 

5.1  26.01  26.11  26.21  26.32  26.42  26.52  26.63  26.73  26.83  26.94 

5.2  27.04  27.14  27.25  27.35  27.46  27.56  27.67  27.77  27.88  27.98 

5.3  28.09  28.20  28.30  28.41  28.52  28.62  28.73  28.84  28.94  29.0c 

5.4  29.16  29.27  29.38  29.48  29.59  29.70  29.81  29.92  30.03  30.14 

5.5  30.25  30.36  30.47  30.58  30.69  30.80  30.91  31.02  31.14  31.25  » 

5.6  31.36  31.47  31.58  31.70  31.81  31.92  324)4  32.15  32.26  32.38 

5.7  32.49  32.60  32.72  32.83  32.95  33.06  33.18  33.29  33.41  33.52 

5.8  33.64  33.76  33.87  33.99  34.11  34.22  34.34  34.46  34.57  34.69 
59  34.81  34.93  35.05  35,16  35.28  35.40  35.52  35.64  35.76  35.88 
6(1  36.00  36.12  66.24  36.36  36.48  36.60  3672  36.84  56.97  3709 


Tables,  C. 
0 


Squares. 
3456 


8 


805 
9  on. 


6.0  36.00  3612  36.24  3636  36.48  36.60  36.72  36.84  36.97  37.091 

6.1  37.21  37.33  37.45  37.58  37.70  37.82  37.95  38.07  38.19  38.32 

6.2  38.44  38.56  38.69  38.81  38.94  39.06  39.19  39.31  39.44  39.56 

6.3  39.69  39.82  39.94  40.07  40.20  40.32  40.45  40.58  40.70  40.83 

6.4  40.96  41.09  41.22  41.34  41.47  41.60  41.73  41.86  41.99  42.12 


6.5 
6.6 
6.7 
6.8 
6.9 

7.0 
7.1 
7.2 
7.3 
7.4 

7.5 
7.6 

7.7 
7.8 
7.9 

8.0 
8.1 
8.2 
8.3 
8.4 

85 
86 
8.7 
88 
8.9 

9.0 
91 
9.2 
9.3 
9.4 


42.25  42.38 

43.56  43.69 

44.89  45.02 

46.24  46.38 

47.61  47.75 


42.51 
43.82 
45.16 
46.51 

47.89 


49.00  49.14  49.28 

50.41  50.55  50.69 

51.84  51.08  52.13 

53.29  53.44  53.58 

54.76  54.91  55.06 


42.64 
43.96 
45.29 
46.65 
48.02 

49.42 
50.84 
52.27 
53.73 
55.20 


42.77 
44.09 
45.43 
46.79 
48.16 

49.56 
50.98 
52.42 

53.88 
55.35 


56.25 
57.76 
59.29 
60.84 
62.41 

64.00 
65.61 
67.24 
68.89 
70.56 

72.25 
73.96 
75.69 
77.44 
79.21 


56.40  56.55.56.70  56.85 

57.91  58.06  58.22  58.37 

59.44  59.60  59.75  59.91 

61.00  61.15  61.31  61.47 

62.57  62.73  62.88  63.04 

64.16  64.32  64.48  64.64 

65.77  65.93  66.10  66.26 

67.40  67.57  67.73  67.90 

6906  69.22  69.39  69.56 

7073  70.90  71.06  71.23 


72.42 
74.13 
75.86 
77.62 
79.39 


81.00  81.18 

82.81  82.99 

84.64  84.82 

86.49  86.68 

88.36  88.55 


72.59 
74.30 
76.04 
77.79 
79.57 

81.36 
83.17 
85.01 

86.86 

88.74 


72.76 
74.48 
76.21 
77.97 
79.74 

81.54 
83.36 
85.19 

87.05 
88.92 


72.93 
74.65 
76.39 
78.15 
79.92 

81.72 

83.54 
85.38 
87.24 
89.11 


42.90 
44.22 
45.56 
46.92 
48.30 

49.70 
51.12 
52.56 
5402 
55.50 

57.00 
58.52 
60.06 
61.62 
63.20 

64.80 
6642 
68.06 
69.72 
71.40 

73.10 

74.82 
76.56 
78.32 
80.10 

81.90 
83.72 
85.56 
87.42 

89.30 


43.03 
44.36 
45.70 
47.06 
48.44 

49.84 
51.27 
52.71 
54.17 
55.65 

57.15 

58.68 
60.22 
61.78 
63.36 

64.96 
66.59 
68.23 
69.89 
71.57 


43.16 
44.49 
45.83 
47.20 

48.58 

49.98 
51.41 
52.85 
54.32 
55.80 

57.30 
58.83 
60.37 
61.94 
63.52 

65.12 
66.75 
68.39 
70.06 
71.74 


43.30 
44.62 
45.97 
47.33 

48.72 

50.13 
51.55 
53.00 
54.46 
55.95 

57.46 
58.98 
60.53 
62.09 
63.68 

65.29 
66.91 
68.56 
70.22 
71.91 


43.43  1» 
44.76 
46.10 
47.47 

48.86 

50.27  u 

51.70 

53.14 

54.61 

56.10 

57.61* 
59.14 

60.68 
62.25 
63.84 

654516- 
67.08 
68.72 
70.39 

72.08 


73.27  73.44 
75.0(f  75.17 
76.74   76.91 
78.50   78.68 

80.28  80.46 


73.62  73.79  1T 

75.34  75.52 

77.09  77.26 

78.85  79.03 

80.64  80.82 


82.08 
83.91 
85,75 
87.61 

89.49 


82.26 
84.09 
85.93 

87.80 
89.68 


82.45 
84.27 
86.12 

87.98 
89.87 


82.63  »•• 
84.46 

86.30 
88.17 
90.06 


9.5  90.25  90.44  90.63  90.82  91.01  91.20  91.39  91.58  91.78  91,97 1» 

9.6  92.16  92.35  92.54  92.74  92.93  93.12  93.32  93.51  93.70  93.90 

9.7  9409  94.28  94.48  94.67  94.87  95.06  95.26  95.45  95.65  95.84 

9.8  96.04  96.24  96.43  96.63  96.83  97.02  97.22  97.42  97.61  97.81 

9.9  98.01  98.21  98.41  98.60  98.80  99.00  99.20  99.40  99.60  99.80 

10.0100.00  100.20  100.40  100.60  100.80  101.00  101.20  101.40  101.61 101.81 20 
10.1  102.01 102  21  102.41  102.62  102.82  103.02  103.23  103.43  103.63  103.84 
10.2 104.04  104.24  104.45  104  65  104.86  105.06  105.27  105.47  105.68  105.88 
10.3  106.09  106.30  106.50  106-71  106.92  107.12  107.33  107.54  107.74  107.95 
10.4108.16  108.37  108.58  108-78  108.99  109.20  109.41  109.62  109.83  110.04 

10.5 110.25  110.46  110.67  110.88  111.09  111,30  111.51 111.72  111.94  112.15* 
10.6112.36  112.57  112.78  113.00  113.21  113.42  113.64  113.85  114.06  114.28 
10.7  114.49  114.70  114.92  115.13  115  35  115.56  115.78  115.99  116  21  116.42 
10.8116.64  116.86  117.07  117.29  117.51  117.72  117.94  118.16  118.37  118.59 
10.9 118.81  119.03  119.25  119.46  119.68  119.90  120.12  120.34  120.56  120.78 
11.0  121.00  121.22  121.44  121.66  121.88  122.10  122,32  122.54  122.77  122.99" 


806 

M 
1.0 

1.1 

1.2 
1.3 
1.4 

1.5 
1.6 
1.7 
1.8 

1.9 

0 

1.000 
1.331 
1.728 
2.197 
2.744 

3.375 
4.096 
4.913 
5.832 
6.859 

1 

1.030 
1.368 
1.772 
2,248 
2.803 

3.443 
4.173 
5.000 
5.930 
6.968 

2 

1.061 
1.405 
1.816 
2.300 
2.863 

3.512 
4.252 

5.088 
6.029 
7.078 

3 

1.093 
1.443 
1.861 
2.353 
2.924 

3.582 
4.331 
5.178 
6.128 
7.189 

Cubes. 

4          5 

1.125   1.158 
1.482   1.521 
1.907    1.953 
2.406   2.460 
2.986  3.049 

3.652  3.724 
4.411   4492 
5.268   5.359 
6.230   6.332 
7.301    7,415 

6 

1.191 
1.561 
2.000 
2.515 
3.112 

3.796 
4.574 
5.452 
6.435 
7.530 

7 

1.225 
1.602 
2.048 
2.571 
3.177 

3.870 
4.657 
5.545 
6.539 
7.645 

Table  3, 
8        9 

1.260   1.295 
1.643   1.655 
2.097   2.147 
2.628  2686 
3.242   3.308 

3.944  4.020 
4.742   4.827 
5.640  5.735 
6.645   6.761 

7.762   7.881 

D. 

33 
CL> 
47 
H 

n 

TS 

M 
Oi 
101 
1H 

2.0  8.000  8.121  8.242  8.365  8.490  8.615  8.742  8.870  8.999  9.120  m 

2.1  9.261  9.394  9.528  9.664  9,800  9.938  10.08  10.22  10.36  10.50  - 

2.2  10.65  10.79  10.94  11.09  11.24  11.39  1154  11.70  11.85  12.01  15 

2.3  12.17  12.33  12.49  12.65  12.81  12.98  13.14  13.31  13.48  13.65  16 

2.4  13.82  14.00  14.17  14.35  14.53  14.71  14.89  15.07  15.25  15.44  18 

2.5  15.63  15.81  16.00  16.19  16.39  16.58  16.78  16.97  17.17  17.37  l9 

2.6  17.58  17.78  17.98  18.19  18.40  18.61  18.82  19.03  19.25  19.47  8t 

2.7  19.68  19.90  20.12  20.35  20.57  20.80  21.02  21.25  21.48  21.72  22 

2.8  21.95  22.19  22.43  22.67  22.91  23.15  23.39  23.64  23.89  24.14  a* 

2.9  24.39  24.64  24.90  25.15  25.41  25.67  25.93  26.20  26.46  26.73  *6 

8.0  27.00  27.27  27.54  27.82  28.09  28.37  28.65  28.93  29.22  29.50  28 

3.1  29.79  30.08  30.37  30.66  30.96  31.26  31.55  31.86  32.16  32.46  80 

3.2  32.77  33.08  33.39  33.70  34.01  34.33  34.65  34.97  35.29  35.61  82 

3.3  35.94  36.26  36.59  36.93  37.26  37.60  37.93  38.27  38.61  38.96  84 

3.4  39,30  39.65  40.00  40.35  40.71  41.06  41.42  41.78  42.14  42.51  86 

3.5  4288  43.24  43.61  43.99  44.36  44.74  45.12  45.50  45.88  46.27  38 

3.6  46.66  47.05  47.44  47.83  48.23  48.63  49.03  49.43  49.84  50.24  40 

3.7  50.65  51.06  51.48  51.90  52.31  52.73  63.16  53.58  54.01  54.44  *2 

3.8  54.87  55.31  55.74  56.18  56.62  57.07  57.51  57.96  58.41  58.86  " 

3.9  59.32  59.78  60.24  60.70  61.16  61.63  62.10  62.57  63.04  63.52  47 

4.0  64,00  64.48  6496  65.45  65.94  66.43  66.92  67.42  67.92  68.42  49 

4.1  68.92  69.43  69.93  70.44  70.96  71.47  71.99  72.51  73.03  73.56  52 

4.2  74.09  74.62  75.15  75.69  76.23  76.77  77.31  77.85  78.40  78.95  8* 

4.3  79.51  80.06  80.62  81.18  81,75  82.31  82.88  83.45  84.03  84.60  67 

4.4  85.18  85.77  86.35  86.94  87.53  88.12  88.72  89.31  89.92  90.52  60 


4.5 

91.13 

91.73 

92.35 

92.96 

93.58 

94.20 

94.82 

95.44 

96.07 

96.70 

M 

4.6 

97.34 

97.97 

98.61 

99.25 

99.90 

100.6 

101.2 

101.8 

102.5 

103.2 

— 

4.7 

103.8 

104.5 

105,2 

105.8 

106.5 

107.2 

107.9 

108.5 

109,2 

109.9 

4.8 

110.6 

111.3 

112.0 

112.7 

113.4 

114.1 

114.8 

115.5 

1162 

116.9 

4.9 

117.6 

118.4 

119.1 

119.8 

120.6 

121.3 

122.0 

122.8 

123.5 

124.3 

5.0 

125.0 

125.8 

126.5 

127.3 

128.0 

128.8 

129.6 

130.3 

131.1 

131.9 

5.1 

132.7 

133.4 

134.2 

135.0 

135.8 

136.6 

137.4 

138.2 

139.0 

139.8 

5.2 

140.6 

141.4 

142.2 

143.1 

143.9 

144.7 

145.5 

146.4 

147.2 

148.0 

5,3 

148.9 

149.7 

150.6 

151.4 

152.3 

153.1 

154.0 

154.9 

155.7 

156.6 

5.4 

157.5 

158.3 

159.2 

160.1 

161.0 

161.9 

162.8 

163.7 

164.6 

165.5 

9 

6.5 

166.4 

167.3 

168.2 

169.1 

170.0 

171.0 

171.9 

172.8 

173.7 

174.7 

? 

5.6 

175.6 

176.6 

177.5 

178.5 

179.4 

180.4 

181.3 

182.3 

183.3 

184.2 

10 

5.7 

185.2 

186.2 

187.1 

188.1 

189.1 

190.1 

191.1 

192.1 

193.1 

194.1 

10 

5.8 

195.1 

196.1 

197.1 

198.2 

199.2 

200.2 

201.2 

202.3 

203.3 

204.3 

10 

5.9 

205.4 

206.4 

207.5 

208.5 

209.6 

210.6 

211.7 

212.8 

213.8 

214.9 

11 

6.0 

216.0 

217.1 

218.2 

219.3 

220.3 

221.4 

222.5 

223.6 

224.8 

225.9 

ki 

Table  3,  D.  Cubes.  SOT 

0         I         23         45         6         789  ML 

6.0  216.0  217.1  218.2  219.3  220.3  221.4  222.5  223.6  224.8  225.9  " 

€.1  227.0  228.1  229.2  230.3  231.5  232.6  233.7  234.9  236.0  237.2  » 

6.2  238.3  239.5  240.6  241.8  243.0  244.1  245.3  246.5  247.7  248.9  12 

C.3  250.0  251.2  252.4  253.6  254.8  256.0  257.3  258.5  259.7  260.9  l2 

6.4  262.1  263.4  264.6  265.8  267.1  268.3  269.6  270.8  272.1  273.4 ia 

6.5  274.6  275.9  277.2  278.4  279.7  281.0  282.3  283.6  284.9  286.2  » 

6.6  287.5  288.8  2901  291.4  292.8  294.1  295.4  296.7  298.1  299.4 l$ 

6.7  300.8  302.1  303.5  304.8  306.2  307.5  308.9  310.3  311.7  313.0  " 

6.8  314.4  315.8  317.2  318.6  320.0  321.4  322.8  324.2  325.7  327.1  l* 

6.9  328.5  329.9  331.4  332.8  334.3  335.7  337.2  338.6  340.1  341.5  " 

7.0  343.0  344.5  345.9  347.4  348.9  350.4  351*9  353.4  354.9  356.4" 

7.1  357.9  359.4  360.9  362.5  364.0  365.5  367*1  368.6  370.1  371.7  " 

7.2  373.2  374.8  376.4  377.9  379.5  381.1  382.7  384.2  385.8  387.4  ie 

7.3  389.0  390.6  392.2  393.8  395.4  397.1  398.7  400.3  401.9  403.6 M 

7.4  405.2  406.9  408.5  410.2  411.8  413.5  415.2  416.8  418.5  420.2  w 

7.5  421.9  423.6  425.3  427.0  428.7  430.4  432.1  433.8  435.5  437.2  « 

7.6  439.0  440.7  442.5  444.2  445.9  447.7  449.5  451.2  453.0  454.8  " 

7.7  456.5  458.3  460.1  461.9  463.7  465.5  467.3  469.1  470.9  472.7  » 

7.8  474.6  476.4  478.2  480.0  481.9  483.7  485.6  487.4  489.3  491.2  1$ 

7.9  493.0  494.9  496.8  498.7  500.6  502.5  504.4  506.3  508.2  510.1  » 

8.0  512.0  513.9  515.8  517.8  519.7  521.7  523.6  525.6  527.5  529.5 19 

8.1  531.4  533.4  535.4  537.4  539.4  541.3  543.3  545.3  547.3  549.4  20 

8.2  551.4  553.4  555.4  557.4  559.5  561.5  563.6  565.6  567.7  569.7  20 

8.3  571.8  573.9  575.9  578.0  580.1  582.2  584.3  586.4  588.5  590.6  2t 

8.4  592.7  594.8  596.9  599.1  601.2  603.4  605.5  607.6  609.8  612.0 21 

£.5  614,1  616.3  618.5  620.7  622.8  625.0  627.2  629.4  631.6  633.8 22 

5.6  636.1  638.3  640.5  642.7  645.0  647.2  649.5  651.7  654.0  656.2 » 

8.7  658.5  660.8  663.1  665.3  667.6  669.9  672.2  674.5  676.8  679.2 2S 

8.8  681.5  683.8  686.1  688.5  690.8  693.2  695.5  697.9  700.2  702.6 2S 

8.9  705.0  707.3  709.7  712.1  714.5  716.9  719.3  721.7  724.2  726.6" 

9.0  729.0  731.4  733.9  736.3  738.8  741.2  743.7  746.1  748.6  751.1  25 

9.1  753.6  756.1  758.6  761.0  763.6  766.1  768.6  771.1  773.6  776.2 25 

9.2  778.7  781.2  783.8  786.3  788.9  791.5  794.0  796.6  799.2  801.8  M 

9.3  804.4  807.0  809.6  812.2  814.8  817.4  820.0  822.7  825.3  827.9  M 

9.4  830.6  833.2  835.9  838.6  841.2  843.9  846.6  849.3  852.0  854.7 2T 

9.5  857.4  850.1  862.8  865.5  868.3  871.0  873.7  876.5  879.2  882.0 2T 

9.6  884.7  887.5  890.3  893.1  895.8  898.6  901.4  904.2  907.0  909.9 M 

9.7  912.7  915.5  918.3  921.2  924.0  926.9  929.7  932.6  935.4  938.3 28 

9.8  941.2  944.1  947.0  949.9  952.8  955.7  958.6  961.5  964.4  967.4 29 

9.9  970.3  973.2  976.2  979.1  982.1  985.1  988.0  991.0  994.0  997.0 3C 

10.01000.0  1003.0  1006.0  1009.0  1012.0  1015.1  1018.1  1021.1  1024.2 1027.2  80 
10.1  1030.3  1033.4  1036.4  1039.5  1042.6  1045.7  1048.8  1051.9  1055.0 1058.1  3l 
10.21061.2  1064.3  1067.5  1070.6  1073.7  107.69  1080.0  1083.2  1086.41089.5  S1 
10.3  1092.7  1095.9'  1099.1  1102.3  1105.5  1108.7  1111.9  1115.2  1118.4 1121.6  8* 
10.41124.9  1128.1  1131.4  1134.6  1137.9  1141.2  1144.4  1147.7  1151.0 1154.3  «• 

10.5 1157.6  1160.9  1164.3  1167.6  1170.9  1174.2  1177.6  1180.9  1184.3  1187.6  8* 
10.6 1191.0 1194.4 1197.8  1201.2  1204.6  1207.9  1211.4 1214.8  1218.2  1221.6  M 
10.7  1225.0  1228.5  1231.9  1235.4  1238.8  1242.3  1245.8  1249.2  1252.7  1256.2  » 

10.81259.7  1263.2  1266.7  1270.2  1273.8  1277.3  1280.8  1284.4  1287.9  1291.5  » 
10.9 1295.0  1298.6  1302.2  1305.8  1309.3  1312.9  1316.5  1320.1 1323.8  1327.4  86 
11.0 1331.0  1334.6  1338.3  1341.9  1345.6  1349.2  1352.9  1356.6  1360.3  1363.9  8T 


808 


Circumferences  of  Circles. 


Table  3,  F. 


10 

11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 


1.  00*  10*  20*  30*  40*  50*  60*  70*  80*  90* 

3142  3173  3204  3236  3267  3299  3330  3362  3393  3424 

3456  3487  3519  3550  3581  3613  3644  3676  3707  3738 

3770  3801  3833  3864  3896  3927  3958  3990  4021  4053 

4084  4115  4147  4178  4210  4241  4273  4304  4335  4367 

4398  4430  4461  4492  4524  4555  4587  4618  4650  4681 


4712 
5027 
5341 
5655 
5969 

6283 
6597 
6912 
7226 
7540 


4744  4775 

5058  5089 

5372  5404 

5686  5718 

6000  6032 

6315  6346 

6629  6660 

6943  6974 

7257  7288 

7571  7603 


4807  4838 

5121  5152 

5435  5466 

5749  5781 

6063  6095 

6377  6409 

6692  6723 

7006  7037 

7320  7351 

7634  7665 


4869 
5184 
5498 
5812 
6126 

6440 
6754 
7069 
7383 
7697 


4901  4932 

5215  5246 

5529  5561 

5843  5875 

6158  6189 

6472  6503 

678(5  6817 

7100  7131 

7414  7446 

7728  7760 


4964  4995 

5278  5309 

5592  5623 

5906  5938 

6220  6252 

6535  6566 

6849  6880 

7163  7194 

7477  7508 

7791  7823 


7854  7885  7917  7948  7980  8011  8042  8074  8105  8137 

8168  8200  8231  8262  8294  8325  8357  8388  8419  8451 

8482  8514  8545  8577  8608  8639  8671  8702  8734  8765 

8796  8828  8859  8891  8922  8954  8985  9016  9048  9079 

9111  9142  9173  9205  9236  9268  9299  9331  9362  9393 


30  9425  9456  9488  9519  9550  9582  9613  9645  9676  9708 

31  9739  9770  9802  9833  9865  9896  9927  9959  9990  10022 

32  10053  10085  10116  10147  10179  10210  10242  10273  10304  10336 

33  10367  10399  10430  10462  10493  10524  10556  10587  10619  10650 

34  10681  10713  10744  10776  10807  10838  10870  10901  10933  10964 

85  10996  11027  11058  11090  11121  11153  11184  11215  11247  11278 

36  11310  11341  11373  11404  11435  11467  11498  11530  11561  11592 

37  11624  11655  11687  11718  11750  11781  11812  11844  11875  11907 

38  11938  11969  12001  12032  12064  12095  12127  12158  12189  12221 

39  12252  12284  12315  12346  12378  12409  12441  12472  12504  12535 


40 

12566 

12598 

12629 

12661 

12692 

12723 

12755 

12786 

12818 

12849 

41 

12881 

12912 

12943 

12975 

13006 

13038 

13069 

13100 

13132 

13163 

42 

13195 

13226 

13258 

13289 

13320 

13352 

13383 

13415 

13446 

13477 

43 

13509 

13540 

13572 

13603 

13635 

13666 

13697 

13729 

13760 

13792 

44 

13823 

13854 

13886 

13917 

13949 

13980 

14012 

14043 

14074 

14106 

45 

14137 

14169 

14200 

14231 

14263 

14294 

14326 

14357 

14388 

14420 

46 

14451 

14483 

14514 

14546 

14577 

14608 

14640 

14671 

14703 

14734 

47 

14765 

14797 

14828 

14860 

14891 

14923 

14954 

14985 

15017 

15048 

48 

15080 

15111 

15142 

15174 

15205 

15237 

15268 

15300 

15331 

15362 

49 

15394 

15425 

15457 

15488 

15519 

15551 

15582 

15614 

15645 

15677 

50 

15708 

15739 

15771 

15802 

15834 

15865 

15896 

15928 

15959 

15991 

51 

16022 

16054 

16085 

16116 

16148 

16179 

16211 

16242 

16273 

16305 

52 

16336 

16368 

16399 

16431 

16462 

16493 

16525 

16556 

16588 

16619 

53 

16650 

16682 

16713 

16745 

16776 

16808 

16839 

16870 

16902 

16933 

54 

16965 

16996 

17027 

17059 

17090 

17122 

17153 

17185 

17216 

17247 

55 

17279 

17310 

17342 

17373 

17404 

17436 

17467 

17499 

17530 

17562 

fill. 

(Mean) 

(i) 
ft 

(2) 

«} 

(4) 
13 

(5) 
16 

(6) 
19 

(7) 
22 

(8) 
25 

(9) 
II 

iable3,F. 


Circumferences  of  Circles. 


809 


Dial.  00*  10*  20,   30*   40*   50*  60*   70*   80*   90* 

55  17279  17310  17342  17373  17404  17436  17467  17499  17530  17562 

56  17593  17624  17656  17687  17719  17750  17781  17813  17844  17876 

57  17907  17938  17970  18001  18033  18064  18096  18127  18158  18190 

58  18221  18253  18284  18315  18347  18378  18410  18441  18473  18504 

59  18535  18567  18598  18630  18661  18692  18724  18755  18787  18818 

60  18850  18881  18912  18944  18975  19007  19038  19069  19101  19132 

61  19164  19195  19227  19258  19289  19321  19352  19384  19415  19446 

62  19478  19509  19541  19572  19604  19635  19666  19698  19729  19761 

63  19792  19823  19855  19886  19918  19949  19981  20012  20043  20075 

64  20106  20138  20169  20200  20232  20263  20295  20326  20358  20389 

65  20420  20452  20483  20515  20546  20577  20609  20640  20672  20703 

66  20735  20766  20797  20829  20860  20892  20923  20954  20986  21017 

67  21049  21080  21112  21143  21174  21206  21237  21269  21300  21331 

68  21363  21394  21426  21457  21488  21520  21551  21583  21614  21646 

69  21677  21708  21740  21771  21803  21834  21865  21897  21928  21960 

70  21991  22023  22054  22085  22117  22148  22180  22211  22242  22274 

71  22305  22337  22368  22400  22431  22462  22494  22525  22557  22588 

72  22619  22651  22682  22714  22745  22777  22808  22839  22871  22902 

73  22934  22965  22996  23028  23059  23091  23122  23154  23185  23216 

74  23248  23279  23311  23342  23373  23405  23436  23468  23499  23531 


75  23562 

76  23876 

77  24190 

78  24504 

79  24819 


23593  23625 
23908  23939 
24222  24253 
24536  24567 
24850  24881 


23656  23688 
23970  24002 
24285  24316 
24599  24630 
24913  24944 


23719  23750 
24033  24065 
24347  24379 
24662  24693 
24976  25007 


23782  23813  23845 

24096  24127  24159 

24410  24442  24473 

24724  24756  24787 

25038  25070  25101 


80  25133  25164  25196  25227  25258  25290  25321  25353  25384  25415 

81  25447  25478  25510  25541  25573  25604  25635  25667  25698  25730 

82  25761  25792  25824  25855  25887  25918  25950  25981  26012  26044 

83  26075  26107  26138  26169  26201  26232  26264  26295  26327  26358 

84  26389  26421  26452  26484  26515  26546  26578  26609  26641  26672 

85  26704  26735  26766  26798  26829  26861  26892  26923  26955  26986 

86  27018  27049  27081  27112  27143  27175  27206  27238  27269  27300 

87  27332  27363  27395  27426  27458  27489  27520  27552  27583  27615 

88  27646  27677  27709  27740  27772  27803  27835  27866  27897  27929 

89  27960  27992  28023  28054  28086  28117  28149  28180  28212  28243 

90  28274  28306  28337  28369  28400  28431  28463  28494  28526  28557 

91  28588  28620  28651  28683  28714  28746  28777  28808  28840  28871 

92  28903  28934  28965  28997  29028  29060  29091  29123  29154  29185 

93  29217  29248  29280  29311  29342  29374  29405  29437  29468  29500 

94  29531  -29562  29594  29625  29657  29688  29719  29751  29782  29814 


95  29845  29877 

96  30159  30191 

97  30473  30505 

98  30788  30819 

99  31102  31133 
100  31416  31447 


29908 
30222 
30536 
30850 
31165 
31479 


Oil,  (Mean) 


29939 
30254 
30568 
30882 
31196 
31510 

(3) 


29971  30002 
30285  30316 
30599  30631 
30913  30945 
31227  31259 
31542  31573 


30034  30065 
30348  30379 
30662  30693 
30976  31008 
31290  31322 
31604  31636 


30096  30128 
30411  30442 
30725  30756 
31039  31070 
31353  31385 
31667  31699 


(4) 
13 


(5) 
It 


(6) 
19 


(7) 


(8) 


810  Areas  of  Circles.  Table  3,  a 

Diai.  *o      a     «s  «3  A  *5  ,6      .1      ,8  ,9    •». 

10  78.5  80.1  81.7  83.3  84.9  86.6  88.2  89.9  91.6  93.3  » 

11  95.0  96.8  98.5  100.3  102.1  103.9  105.7  107.5  109.4  111.2  18 

12  113.1  115.0  116.9  118.8  120.8  122.7  124.7  126.7  128.7  130.7  20 

13  132.7  134.8  136.8  138.9  141.0  143.1  145.3  147.4  149.6  151.7  21 

14  153.9  156.1  158.4  160.6  162.9  165.1  167.4  169.7  172.0  174.4  23 

15  176.7  179.1  181.5  183.9  1863  188.7  191.1  193.6  196.1  198.6  24 

16  201.1  203.6  206.1  208.7  211.2  213.8  216.4  219.0  221.7  224.3  26 

17  227.0  229.7  232.4  235.1  237.8  2405  243.3  246.1  248.8  251.6  28 

18  254.5  257.3  260.2  263.0  265.9  268.8  271.7  274.6  277.6  2806  2a 

19  283.5  286.5  289.5  292.6  295.6  298.6  301.7  304.8  307.9  311.0  " 

20  314.2  317.3  320.5  323.7  326.9  330.1  333.3  336.5  339.8  343.1  M 

21  346.4  349.7  353.0  356.3  359.7  363.1  366.4  369.8  373.3  376.7  84 

22  380.1  383.6  387.1  390.6  394.1  397.6  401.1  404.7  408.3  411.9  M 

23  415.5  419.1  422.7  426.4  430.1  433.7  437.4  441.2  444.9  448  6  " 

24  452.4  456.2  460.0  4638  467.6  471.4  475.3  479.2  483.1  487.0  38 

25  490.9  494.8  498.8  502.7  506.7  510.7  514.7  518.7  522.8  526.9  40 
20  530.9  535.0  539.1  543.3  547.4  551.5  555.7  559.9  564.1  568.3  4a 

27  572.6  576.8  581.1  585.3  589.6  594.0  598.3  602.6  607.0  611.4  49 

28  615.8  620.2  624.6  629.0  633.5  637.9  642.4  646.9  651.4  656.0  43 

29  660.5  665.1  669.7  674.3  678.9  683.5  688.1  692.8  697.5  702.2  46 

30  706,9  711.6  716.3  721.1  725,8  730.6  735.4  740.2  745.1  749.9  48 

31  754.8  759.6  764.5  769.4  774.4  779.3  784.3  789.2  794.2  799.2  50 

32  804.2  809.3  814.3  819.4  824.5  829.6  834.7  839.8  845.0  850.1  51 

33  855.3  860.5  865.7  870.9  876.2  881.4  886.7  892.0  897.3  902.6  5S 

34  907.9  913.3  918.6  924.0  929.4  934.8  940.2  945.7  951.1  956,6  54 

35  962   968   973   979  984   990  995  1001  1007  1012 

36  1018  1024  1029  1035  1041  1046  1052  1058  1064  1069 

37  1075  1081  1087  1093  1099  1104  1110  1116  1122  1128 

38  1134  1140  1146  1152  1158  1164  1170  1176  1182  1188  6 

39  1195  1201  1207  1213  1219  1225  1232  1238  1244  1250 

40  1257  1263  1269  1276  1282  1288  1295  1301  1307  1314 

41  1320  1327  1333  1340  1346  1353  1359  1366  1372  1379 

42  1385  1392  1399  1405  1412  1419  1425  1432  1439  1445 

43  1452  1459  1466  1473  1479  1486  1493  1500  1507  1511 

44  1521  1527  1534  1541  1548  1555  1562  1569  1576  1583 

45  1590  1598  1605  1612  1619  1626  1633  1640  1647  1655  ' 

46  1662  1669  1676  1684  1691  1698  1706  1713  1720  1728 

47  1735  1742  1750  1757  1765  1772  1780  1787  1795  1802 

48  1810  1817  1825  1832  1840  1847  1855  1863  1870  1878 

49  1886  1893  1901  1909  1917  1924  1932  1940  1948  1956 

50  1963  1971  1979  1987  1995  2003  2011  2019  2027  2035 

51  2043  2051  2059  2067  2075  2083  2091  2099  2107  2116  • 

52  2124  2132  2140  2148  2157  2165  2173  2181  2190  2198 

53  2206  2215  2223  2231  2240  2248  2256  2265  2273  2282 

54  2290  2299  2307  2316  2324  2333  2341  2350  2359  2367 

55  2376  2384  2393  2402  2411  2419  2428  2437  2445  2454 


rabie  3,  Q.                      Areas  of  Circles.  811 

Diam,  .0  «1  ,2  ,3  ,4  «5   46  4?  48  49  Dif. 

55  2376  2384  2393  2402  2411  2419  2428  2437  2445  2454 

56  2463  2472  2481  2489  2498  2507  2516  2525  2534  2543 

57  2552  2561  2570  2579  2588  2597  2606  2615  2624  2633  a 

58  2642  2651  2660  2669  2679  2688  2697  2706  2715  2725 

59  2734  2743  2753  2762  2771  2781  2790  2799  2809  2818 

60  2827  2837  2846  2856  2865  2875  2884  2894  2903  2913 

61  2922  2932  2942  2951  2961  2971  2980  2990  3000  3009 

62  3019  3029  3039  3048  3058  3068  3078  3088  3097  3107 

63  3117  3127  3137  3147  3157  3167  3177  3187  3197  3207 

64  3217  3227  3237  3247  3257  3267  3278  3288  3298  3308  ia 

65  3318  3329  3339  3349  3359  3370  3380  3390  3400  3411 

66  3421  3432  3442  3452  3463  3473  3484  3494  3505  3515 

67  3526  3536  3547  3557  3568  3578  3589  3GOO  3610  3621 

68  3632  3642  3653  3664  3675  3685  3696  3707  3718  3728 

69  3739  3750  3761  3772  3783  3794  3805  3816  3826  3837 

70  3848  3859  3871  3882  3893  3904  3915  3926  3937  3948" 

71  3959  3970  3982  3993  4004  4015  4026  4038  4049  4060 

72  4072  4083  4094  4106  4117  4128  4140  4151  4162  4174 

73  4185  4197  4208  4220  4231  4243  4254  4266  4278  4289 

74  4301  4312  4324  4336  4347  4359  4371  4383  4394  4406 

75  4418  4430  4441  4453  4465  4477  4489  4501  4513  4524 

76  4536  4548  4560  4572  4584  4596  4608  4620  4632  4645  » 

77  4657  4669  4681  4693  4705  4717  4729  4V42  4754  4766 

78  4778  4791  4803  4815  4827  4840  4852  4865  4877  4889 

79  4902  4914  4927  4939  4951  4964  4976  4989  5001  5014 

80  5027  5039  5052  5064  5077  5090  5102  5115  5128  5140 

81  5153  5166  5178  5191  5204  5217  5230  5242  5255  5268 

82  5281  5294  5307  5320  5333  5346  5359  5372  5385  5398  1S 

83  5411  5424  5437  5450  5463  5476  5489  5502  5515  5529 

84  5542  5555  5568  5581  5595  5608  5621  5635  5648  5661 

85  5675  5638  5701  5715  5728  5741  5755  5768  5782  5795 

86  5809  5822  5836  5849  5863  5877  5890  5904  5917  5931 

87  5945  5958  5972  5986  5999  6013  6027  6041  6055  6068 

88  6082  6096  6110  6124  6138  6151  6165  6179  6193  6207 

89  6221  6235  6249  6263  6277  6291  6305  6319  6333  6348  u 

90  6362  6376  6390  6404  6418  6433  6447  6461  6475  6490 

91  6504  6518  6533  6547  6561  6576  6590  6604  6619  6633 

92  6648  6662  6677  6691  6706  6720  6735  6749  6764  6778 

93  6793  6808  6822  6837  6851  6866  6881  6896  6910  6925 

94  6940  6955  6969  6984  6999  7014  7029  7044  7058  7073 

95  7088  7103  7118  7133  7148  7163  7178  7193  7208  7223  ls 

96  7238  7253  7268  7284  7299  7314  7329  7344  7359  7375 

97  7390  7405  7420  7436  7451  7466  7482  7497  7512  7528 

98  7543  7558  7574  7589  7605  7620  7636  7651  7667  7682 

99  7698  7713  7729  7744  7760  7776  7791  7807  7823  7838 
100  7854  7870  7885  7901  7917  7933  7949  7964  7980  7996  lfr 


812 

Volumes  of 

Spheres. 

Table  3, 

H. 

Diam, 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Dif. 

1.0 

.524 

.539 

.556 

.572 

.589 

.606 

.624 

.641 

.660 

.678 

17 

1.1 

.697 

.716 

.736 

.755 

.776 

.796 

.817 

.839 

.860 

,882 

21 

1.2 

.905 

.928 

.951 

.974 

.998 

1.023 

1.047 

1.073 

1.098 

1.124 

26 

1.3 

1.150 

1.177 

1.204 

1.232 

1.260 

1.288 

1.317 

1.346 

1.376 

1.406 

29 

1.4 

1.437 

1.468 

1.499 

1.531 

1.563 

1.596 

1.630 

1.663 

1.697 

1.732 

SS 

1.5 

1.767 

1.803 

1.839 

1.875 

1.912 

1.950 

1.988 

2.026 

2.065 

2.105 

88 

1.6 

2.145 

2.185 

2.226 

2.268 

2.310 

2.352 

2.395 

2.439 

2.483 

2.527 

43 

1.7 

2.572 

2.618 

2.664 

2.711 

2.758 

2.806 

2.855 

2.903 

2.953 

3.003 

18 

1.8 

3.054 

3.105 

3.157 

3.209 

3.262 

3.315 

3.369 

3.424 

3.479 

3.535 

54 

1.9 

3.591 

3.648 

3.706 

3.764 

3.823 

3.882 

3.942 

4.003 

4.064 

4.126 

GO 

20 

4.189 

4.252 

4.316 

4.380 

4.445 

4.511 

4577 

4.644 

4.712 

4.780 

fi6 

21 

4.849 

4.919 

4.989 

5.060 

5.131 

5.204 

5.277 

5.350 

5.425 

5.500 

7', 

2.2 

5.575 

5.652 

5.729 

5.806 

5.885 

5.964 

6.044 

6.125 

6.206 

6.288 

80 

2.3 

6.371 

6.454 

6.538 

6.623 

6.709 

6.795 

6.882 

6.970 

7.059 

7.148 

87 

2.4    7.238   7.329   7.421    7.513   7.606   7.700   7.795   7.890   7.986   8.083  94 


25 
2.6 
2.7 
2.8 
2.9 


8.18  8.28 

9.20  9.31 

10.31  10.42 

11.49  11.62 

12.77  12.90 


8.38 

9.42 

10.54 

11.74 

13.04 


8.48 

9.53 

10.65 

11.87 

13.17 


8.5S 

9.63 

10.77 

11.99 

13.31 


8.68 

9.74 

10.89 

12.12 

13.44 


8.78 

9.85 

11.01 

12.25 

13.58 


8.89 

9.97 

1U3 

12.38 

13.72 


8.99 
10.08 
11.25 
12.51 
13.86 


9.10  10 

10.19  » 

11.87  ia 

12.64  '8 

14.00  u 


3.0  14.14  14.28  14.42  14.57  14.71  14.86  15.00  15.15  15.30  15.45  » 

3.1  15.60  15.75  15.90  16.06  16.21  16.37  16.52  16.68  16.84  17.00  » 

3.2  17.16  17.32  17.48  17.64  17.81  17.97  18.14  18.31  18.48  18.65  « 

3.3  18.82  18.99  19.16  19.33  19.51  19.68  19.86  20.04  20.22  20.40  18 

3.4  20.58  20.76  20.94  21.13  21.31  21.50  21.69  21.88  22.07  22.26  w 


3.5 
3.6 
3.7 
3.8 
3.9 


22.45  22.64 

24.43  24.63 

26.52  26.74 

28.73  28.96 

31.06  31.30 


22.84 
24.84 
26.95 
29.19 
31.54 


23.03 
25.04 
27.17 
29.42 
31.78 


23.23  23.43 

25.25  25.46 

27.39  27.61 

29.65  29.88 

32.02  32.27 


23.62 
25.67 
27.83 
30.11 
32.52 


23.82 
25.88 
28.06 
30.35 
32.76 


24  02  24.23  20 

26.09  26.31  21 

28.28  28.50  22 

30.58  30.82  28 

33.01  33.26  ** 


4.0  33.51   33.76   34.02   34.27   34.53  34.78  35.04  35.30  35.56  35.82  M 

4.1  36.09   36.35   36.62   36  88   37.15  37.42  37.69  37.97  38.24  38.52  " 

4.2  38.79   39.07   39.35   39.63   39.91  40.19  40.48  40.76  41.05  41  34  » 

42.80  43.10  43.40  43.70  44.00  44.30  80 


4.3  41.63  41.92  42.21 

4.4  44.60  44.91   45.21 


42.51 

45.52   45,83   46.14  46.45   46.77   47.08   47.40 


4.5  47.71  48.03  48.35  48.67  49.00  49.32  49.65  49.97  50.30  50.63  * 

4.6  50.97  51.30  51.63  51.97  52.31  52.65  52.99  53.33  53.67  54.02  s* 

4.7  54.36  54.71  55.06  55.41  55.76  56.12  56.47  56.83  57.18  57.54  M 

4.8  57.91  58.27  58.63  59.00  59.37  59.73  60.10  60.48  60.85  61.22  8T 

4.9  61.60  61.98  62.36  62.74  63.12  63.51  63.89  64.28  64.67  65.06  M 

5.0  65.45  65.84  6624  66.64  67.03  67.43  67.83  68:24  68.64  69.05  *° 

5.1  69.46  69.87  70.28  70.69  71.10  71.52  71.94  72.36  72.78  73.20  4t 

5.2  73.62  74.05  74.47  74.90  75.33  75.77  76.20  7664  77.07  77.51  *» 

5.3  77.95  78.39  78.84  79,28  79.73  80.18  80.63  81.08  81.54  81.99  *» 

5.4  82.45  82.91  83.37  83.83  84.29  84.76  85.23  85.70  86.17  86.64  4T 

5.5  87.11  87.59  8807  88.55  89.03  89.51  90.00  90.48  90.97  91.46  a 


Table 

3,H. 

Volumes  of  Spheres. 

813 

Diaa. 

0 

i 

3 

3 

4 

5 

6 

7 

8 

9 

5.5 

87.1 

87.6 

88.1 

88.5 

89.0 

89.5 

90.0 

90.5 

91.0 

91.5Dif. 

5.6 

92.0 

92.4 

92.9 

93.4 

93.9 

94.4 

94.9 

95.4 

95.9 

96.5    fi 

5.7 

97.0 

97.5 

98.0 

98.5 

99.0 

99.5 

100.1 

100.6 

101.1 

101.6 

5.8 

102.2 

102.7 

103.2 

103.8 

104.3 

104.8 

105.4 

105.9 

106.4 

107.0 

59 

107.5 

108.1 

108.6 

109.2 

109.7 

110.3 

110.9 

111.4 

112.0 

112.5 

6.0 

113.1 

113.7 

114.2 

1148 

115.4 

115.9 

116.5 

117.1 

117.7 

118.3 

6.1 

118.8 

119.4 

120.0 

120.6 

121.2 

121.8 

122.4 

123.0 

123.6 

124.2    • 

6.2 

124.8 

125.4 

126.0 

126.6 

127.2 

127.8 

128.4 

129.1 

129.7 

130.3 

6.3 

130.9 

131.5 

132.2 

132.8 

133.4 

134.1 

134.7 

135.3 

136.0 

136.6 

6.4 

137.3 

137.9 

138.5 

139.2 

139.8 

140.5 

141.2 

141.8 

142.5 

143.1 

6.5  143.8  144.5  145.1  145.8  146.5  147.1  147.8  148.5  149  2  149.8 

6.6  150.5  151/2  151.9  152.6  153.3  154.0  154.7  155.4  156.1  156.8   -» 

6.7  157.5  158.2  1589  159.6  160.3  161.0  161.7  162.5  163,2  163.9 

6.8  164.6  165.4  166.1  166.8  167.6  168.3  169.0  169.8  170.5  171.3 

6.9  172.0  172.8  173.5  174.3  175.0  175.8  176.5  177.3  178.1  178.8 

7.0  179.6  180.4  181.1  181.9  182.7  183.5  184.3  185.0  185.8  186.6 

7.1  187.4  188.2  189.0  189.8  190.6  191.4  192.2  193.0  193.8  194.6    • 

7.2  195.4  196.2  197.1  197.9  198.7  199.5  200.4  201.2  202.0  202.9 

7.3  203.7  204.5  205.4  206.2  207.1  207.9  208.8  209.6  210.5  211.3 

7.4  212.2  213.0  213.9  214.8  215.6  216.5  217.4  218.3  219.1  220.0 

7.5  220.9  221.8  222.7  223.6  224.4  225.3  226.2  227.1  228.0  228.9    • 

7.6  229.8  230.8  231.7  232.6  233.5  234.4  235.3  236.3  237.2  238.1 

7.7  239.0  240.0  240.9  241.8  242.8  243.7  244.7  245.6  246.6  247.5 

7.8  248.5  249.4  250.4  251.4  252.3  253.3  254.3  255.2  256.2  257.2 

7.9  258.2  259.1  260.1  261.1  262.1  263.1  264.1  265.1  266.1  267.1  »° 

8.0  268.1  269.1  270.1  271.1  272.1  273.1  274.2  275.2  276.2  277.2 

8.1  278.3  279.3  280.3  281.4  282.4  283.4  284.5  285.5  286.6  287.6 

8.2  288.7  289.8  290.8  291.9  292-9  294.0  295.1  296.2  297.2  298.3 

8.3  299.4  300.5  301.6  302.6  303.7  304.8  305.9  307.0  308.1  309.2  " 

8.4  310.3  311.4  312.6  313.7  314.8  315.9  317.0  318.2  319.3  320.4 

8.5  321.6  322.7  323.8  325.0  326.1  327.3  328.4  329.6  330.7  331.9 

8.6  333.0  334.2  335.4  336.5  337.7  338.9  340.1  341.2  342.4  343.6 

8.7  344.8  346.0  347.2  348.4  349.6  350.8  352.0  353.2  354.4  355.6  18 

8.8  356.8  358.0  359.3  360.5  361.7  362.9  364,2  365.4  366.6  367.9 

8.9  369.1  370.4  371.6  372.9  374.1  375.4  376.6  377.9  379.2  380.4 

9.0  381.7  383.0  384.3  385.5  386.8  388.1  389.4  390.7  392.0  393.3  18 

9.1  394.6  395.9  397.2  398.5  399.8  401.1  402.4  403.7  405.1  4064 

9.2  407.7  409.1  410.4  411.7  413.1  414.4  415.7  417.1  418.4  419.8 

9.3  421.2  422.5  423.9  425.2  426.6  428.0  429.4  430.7  432.1  433.5 
9,4434.9  436.3,437.7  439.1  440.5  441.9  443.3  444.7  4461  447.5  M 


9.5  448.9  450.3 

9.6  463.2  464.7 

9.7  477.9  479.4 

9.8  492.8  494.3 

9.9  508.0 


451.8  453.2  454.6  456.0  457*5  4589  460.4  461.8 

466.1  467.6  469.1  470.5  472.0  475.5  474.9  476.4 

480.8  482.3  483.8  485.3  486.8  488.3  489.8  491.3  » 

495.8  497.3  498.9  500.4  501.9  503.4  505.0  506.5 

511.1  512.7  514.2  515.8  5173  518.9  520.5  522.0 

10.0  523.6  525.2   526.7  528.3  529.9  531.5  533.1  534.7  536.3  537.9  " 


509.6 


814  Natural  Sines.  Table  4. 

Angle   *o     ,1     ,2     .3     «4     «5     *6     .7     «8     *9   Complement  on. 

0°  0.0000  0017  0035  0052  0070  0087  0105  0122  0140  0157  0175  89° 

1  0175  0192  0209  0227  0244  0262  0279  0297  0314  0332  0349  88 

2  0349  0366  0384  0401  0419  0436  0454  0471  0488  0506  0523  87 

3  0523  0541  0558  0576  0593  0610  0628  0645  0663  0680  0698  86 

4  0698  0715  0732  0750  0767  0785  0802  0819  0837  0854  0872  85 

5  0.0872  0889  0906  0924  0941  0958  0976  0993  1011  1028  1045  84 

6  1045  1063  1080  1097  1115  1132  1149  1167  1184  1201  1219  83 

7  1219  1236  1253  1271  1288  1305  1323  1340  1357  1374  1392  82 

8  1392  1409  1426  1444  1461  1478  1495  1513  1530  1547  1564  81 

9  1564  1582  1599  1616  1633  1650  1668  1685  1702  1719  1736  80 

10  0.1736  1754  1771  1788  1805  1822  1840  1857  1874  1891  1908  79 

11  1908  1925  1942  1959  1977  1994  2011  2028  2045  2062  2079  78 

12  2079  2096  2113  2130  2147  2164  2181  2198  2215  2233  2250  77  « 

13  2250  2267  2284  2300  2317  2334  2351  2368  2385  2402  2419  76 

14  2419  2436  2453  2470  2487  2504  2521  2538  2554  2571  2588  75 

15  0.2588  2605  2622  2639  2656  2672  2689  2706  2723  2740  2756  74 

16  2756  2773  2790  2807  2823  2840  2857  2874  2890  2907  2924  73 

17  2924  2940  2957  2974  2990  3007  3024  3040  3057  3074  3090  72 

18  3090  3107  3123  3140  3156  3173  3190  3206  3223  3239  3256  71 

19  3256  3272  3289  3305  3322  3338  3355  3371  3387  3404  3420  70 

20  0.3420  3437  3453  3469  3486  3502  3518  3535  3551  3567  3584  69 

21  3584  3600  3616  3633  3649  3665  3681  3697  3714  3730  3746  68 

22  3746  3762  3778  3795  3811  3827  3843  3859  3875  3891  3907  67 

23  3907  3923  3939  3955  3971  3987  4003  4019  4035  4051  4067  66  '• 

24  4067  4083  4099  4115  4131  4147  4163  4179  4195  4210  4226  65 

25  0.4226  4242  4258  4274  4289  4305  4321  4337  4352  4368  4384  64 

26  4384  4399  4415  4431  4446  4462  4478  4493  4509  4524  4540  63 

27  4540  4555  4571  4586  4602  4617  4633  4648  4664  4679  4695  62 

28  4695  4710  4726  4741  4756  4772  4787  4802  4818  4833  4848  61 

29  4848  4863  4879  4894  4909  4924  4939  4955  4970  4985  5000  60 

30  0.5000  5015  5030  5045  5060  5075  5090  5105  5120  5135  5150  59  » 

31  5150  5165  5180  5195  5210  5225  5240  5255  5270  5284  5299  58 
82  5299  5314  5329  5344  5358  5373  5388  5402  5417  5432  5446  57 

33  5446  5461  5476  5490  5505  5519  5534  5548  5563  5577  5592  56 

34  5592  5606  5621  5635  5650  5664  5678  5693  5707  5721  5736  55 

35  0.5736  5750  5764  5779  5793  5807  5821  5835  5850  5864  5878  54 

36  5878  5892  5906  5920  5934  5948  5962  5976  5990  6004  6018  53  * 

37  6018  6032  6046  6060  6074  6088  6101  6115  6129  6143  6157  52 

38  6157  6170  6184  6198  6211  6225  6239  6252  6266  6280  6293  51 

39  6293  6307  6320  6334  6347  6361  6374  6388  6401  6414  6428  50 

40  0.6428  6441  6455  6468  6481  6494  6508  6521  6534  6547  6561  49 

41  6561  6574  6587  6600  6613  6626  6639  6652 "6665  6678  6691  48  » 

42  6691  6704  6717  6730  6743  6756  6769  6782  6794  6807  6820  47 

43  6820  6833  6845  6858  6871  6884  6896  6909  6921  6934  6947  46 
44°  6947  6959  6972  6984  6997  7009  7022  7034  7046  7059  7071  45° 

•9   ,8   .7   .6   ,5   A   *3   ,2   «1   ,0  Angle 
Natural  Cosines. 


Table  4.  Natural  Sines.  815 

Aflgle    *0       *1      *2      *3      *4      ,5      ,6      .7      *8      *9    Complement  Dif. 

45°  0.7071  7083  7096  7108  7120  7133  7145  7157  7169  7181  7193  44° 

46  7193  7206  7218  7230  7242  7254  7266  7278  7290  7302  7314  43  I8 

47  7314  7325  7337  7349  7361  7373  7385  7396  7408  7420  7431  42 

48  7431  7443  7455  7466  7478  7490  7501  7513  7524  7536  7547  41 

49  7547  7559  7570  7581  7593  7604  7615  7627  7638  7649  7660  40 

50  0.7660  7672  7683  7694  7705  7716  7727  7738  7749  7760  7771  39 

51  7771  7782  7793  7804  7815  7826  7837  7848  7859  7869  7880  38  " 

52  7880  7891  7902  7912  7923  7934  7944  7955  7965  7976  7986  37 

53  7986  7997  8007  8018  8028  8039  8049  8059  8070  8080  8090  36 

54  8090  8100  8111  8121  8131  8141  8151  8161  8171  8181  8192  35 

55  0.8192  8202  8211  8221  8231  8241  8251  8261  8271  8281  8290  84  » 

56  8290  8300  8310  8320  8329  8339  8348  8358  8368  8377  8387  33 

57  8387  8396  8406  8415  8425  8434  8443  8453  8462  8471  8480  32 

58  8480  8490  8499  8508  8517  8526  8536  8545  8554  8563  8572  31 

59  8572  8581  8590  8599  8607  8616  8625  8634  8643  8652  8660  30  9 

60  0.8660  8669  8678  8686  8695  8704  8712  8721  8729  8738  8746  29 

61  8746  8755  8763  8771  8780  8788  8796  8805  8813  8821  8829  28 

62  8829  8838  8846  8854  8862  8870  8878  8886  8894  8902  8910  27  3 

63  8910  8918  8926  8934  8942  8949  8957  8965  8973  8980  8988  26 

64  8988  8996  9003  9011  9018  9026  9033  9041  9048  9056  9063  25 

65  0.9063  9070  9078  9085  9092  9100  9107  9114  9121  9128  9135  24 

66  9135  9143  9150  9157  9164  9171  9178  9184  9191  9198  9205  23  1 

67  9205  9212  9219  9225  9232  9239  9245  9252  9259  9265  9272  22 

68  9272  9278  9285  9291  9298  9304  9311  9317  9323  9330  9336  21 

69  9336  9342  9348  9354  9361  9367  9373  9379  9385  9391  9397  20  8 

70  0.9397  9403  9409  9415  9421  9426  9432  9438  9444  9449  9455  19 

71  9455  9461  9466  9472  9478  9483  9489  9494  9500  9505  9511  18 

72  9511  9516  9521  9527  9532  9537  9542  9548  9553  9558  9563  57 

73  9563  9568  9573  9578  9583  9588  9593  9598  9603  9608  9613  16  • 

74  9613  9617  9622  9627  9632  9636  9641  9646  9650  9655  9659  15 

75  0.9659  9664  9668  9673  9677  9681  9686  9690  9694  9699  9703  14 

76  9703  9707  9711  9715  9720  9724  9728  9732  9736  9740  9744  13  * 

77  9744  9748  9751  9755  9759  9763  9767  9770  9774  9778  9781  12 

78  9781  9785  9789  9792  9796  9799  9803  9806  9810  9813  9816  11 

79  9816  9820  9823  9826  9829  9833  9836  9839  9842  9845  9848  10 

80  0.9848  9851  9854  9857  9860  9863  9866  9869  9871  9874  9877  9  • 

81  9877  9880  9882  9885  9888  9890  9893  9895  9898  9900  9903  8 

82  9W3  9905  9907  9910  9912  9914  9917  9919  9921  9923  9925  7 

83  9925  9928  9930  9932  9934  9936  9938  9940  9942  9943  9945  6  * 

84  9945  9947  9949  9951  9952  9954  9956  9957  9959  9960  9962  5 

85  0.9962  9963  9965  9966  9968  9969  9971  9972  9973  9974  9976  4 

86  9976  9977  9#78  9979  9980  9981  9982  9983  9984  9985  9986  3  > 

87  9986  9987  9988  9989  9990  9990  9991  9992  9993  9993  9994  2 

88  9994  9995  9995  9996  9996  9997  9997  9997  9998  9998  9998  1 
89°  9998  9999  9999  9999  9999  1.0000  1-0000  1-0000  1.0000 1.0000  1.0000  0°  • 

«9  *8   «7  »6  45  >4   *3   *2  4  40  Angle 
Natural  Cosines. 


816  Logarithmic  Sines.  Table  4.  A. 

ingle  .0     .1      J     .3  .4     .5      .6  .7  .8  .9    Complement  oit. 

00l-00  ".2419  ".5429  jT.7190  3.8439  3~9408  2>.0200  2~.0870  2*.1450  2~.1961  2~.2419  89°  — 

1  2*72419  2~.2832  £"3210  2T.3558  2~.38SO  2i4179  £4459  "f.4723  2~.4971  2~!5206  2^542b  88  — 

2  5428   5640   5842   6035  6220   6397   6567  6731  6889  7041   7188  87  — 

3  7188   7330   7468   7602  7731   7857   7979  8098  8213  8326   8436  86  — 

4  8436   8543   8647   8749  8849   8946   9042  9135  9226  9315   9403  85  — 

5  ".9403  2*9489  ".9573  2**9655  279736  2*9816  2*.9894  2~9970  ".0046  "0120  ".0192  84  T£ 

6  ".0192  T.0264  T.0334  l".0403  T.0472  L0539  T".OG05  ".0670  ".0734  T.0797  f.0859  83  * 

7  0859   0920   0981   1040  1099   1157   1214  1271  1326  1381   1436  82  * 

8  1436   1489   1542   1594  1648   1697   1747  1797  1847  1895   1943  81  6 

9  1943   1991   2038   2085  2131   2176   2221  2266  2310  2353   2397  80  ** 

10  ".2397  ".2439  ".2482  ".2524  ".2565  ".2606  ".2647  "2637  "2727  ".2767  ".2806  79  * 

11  2806   2845   2883   2921  2959   2997   8034  3070  3107  8143   3179  78  * 

12  3179   8214   8249   8284  8319   8353   3387  8421  8455  3488   8521  77  34 

13  3521   8554   8586   8618  8650   8682   8713  3745  3775  8806   8837  76  8l 

14  8837   8867   8897   3927  8957   8986   4015  4044  4073  4102   4130  75  49 

15  ".4130  ".4158  ".4186  ".4214  ".4242  ".4269  T.4296  ".4323  T.4350  ".4377  ".4403  74  27 

16  4403   4430   4456   4482  4508   4533   4559  4584  4609  4634   4659  73  26 

17  4659   4684   4709   4733  4757   4781   4805  4829  4353  4876   4900  72  2' 

18  4900   4923   4946   4969  4992   5015   5037  5060  5082  5104   5126  71  2 

19  5126   5148   6170   5192  5213   5235   5256  5278  5299  5320   5341  70  22 

20  ".5341  ".5361  ".5382  ".5402  ".5423  T.5443  ".5463  ".5484  ".5504  ".5523  ".5543  69  2< 

21  5543   5563   5583   5602  5621   5641   5660  5679  5698  5717   5736  68  1! 

22  5736   5754   5773   5792  5810   5828   5847  5865  5883  5901   5919  67  * 

23  5919   5937   5954   5972  5990   6007   6024  6042  6059  6076   6093  66  1( 

24  6093   6110   6127   6144  6161   6177   6194  6210  6227  6243   6259  65  " 

25  f.6259  ".6276  ".6292  ".6308  ".6324  ".6340  ".6356  ".6371  ".6387  Jf.6403  ".6418  64  1( 

26  6418   6434   6449   6465  6430   6495   6510  6526  6541  6556   6570  63  " 

27  6570   6585   6600   6615  6629   6644   6659  6673  6687  6702   6716  62  l* 

28  6716   6730   6744   6759  6773   6787   6801  6314  6828  6342   6856  61  M 

29  6856   6869   6883   6896  6910   6923   6937  6950  6963  6977   6990  60 

30  ".6990  T.7003  T.7016  ".7029  ".7042  ".7055  T.7068  ".7030  ".7093  7.7106  ~7118  59  W 

31  7118   7181   7144   7156  7168   7181   7193  7205  7218  7230   7242  58 

32  7242   7254   7266   7278  7290   7302   7314  7326  7338  7349   7361  57  ** 

33  7361   7373   7384   7396  7407   7419   7430  7442  7453  7464   7476  56 

34  7476   7487   7498   7509  7520   7531   7542  7553  7564  7575   7586  55  ll 

35  ".7586  "7597  T.7607  ".7618  T.7629  ".7640  T.7650  ".7661  ".7671  ".7682  "f.7692  54 

36  7692   7703   7713   7723  7734   7744   7754  7764  7774  7785   7795  53 

87  7795   7805   7815   7825  7835   7844   7854  7864  7874  7884   7893  52  10 

88  7893   7903   7913   7922  7932   7941   7951  7960  7970  7979   7989  51 
39  7989   7998   8007   8017   8026   8035   8044  8053  8063  8072   8081  50 


40  ".8081  ".8090  T.8099  ".8108  ".8117  ".8125  ".8134  ".8143  ".8152  ".8161  7.8169  49   ' 

41  8169   8178   8187   8195  8204   8213   8221   8230   8238  8247  8255  48 

42  8255   8264   8272   8280  8289   8297   8305   8313   8322  8330  8338  47 

43  8338   8346   8354   8362  8370   8378   8386   8394   8402  8410  8418  46 
44°  8418   8426   8433   8441  8449   8457   8464   8472   8480  8437  8495  45°  ' 

Complement    .9      .8     .7  .6     .5     .4     .3      .2  .1  .0  Angle 
Logarithmic  Cosines, 


Table  4.  A.  Logarithmic  Sines.                        817 

Angle  .0     .1      .2  .3      .4  .5      .6     .7  .8     .9    Complement  on. 

45°  '.8495  T.S502  ~8510  "8517  "8525  ~8532  ".8540  ".8547  "8555  lts562  ".8569  44° 

46  8569   8577   8584  8591   8598  8606   8613   8620  8627   8634   8641  43 

47  8641   8648   8655  8662   8669  8676   8683   8690  8697   8704   8711  42  7 

48  8711   8718   8724  8731   8738  8745   8751   8758  8765   8771   8778  41 

49  8778   8784   8791  8797   8804  8810   8317   8823  8830   8836   8843  40 

50  ".8843  ".S849  "8855  "8862  "8868  "8874  ~8880  "8887  ".8893  1^8899  L8905  39 

51  8905   8911   8917  8923   8929  8935   8941   8947  8953   8959   8965  38  6 

52  8965   8971   8977  8983   8989  8995   9000   9006  9012   9018   9023  37 

53  9023   9029   9035  9041   9046  9052   9057   9063  9069   9074   9080  36 

54  9080   9085   9091  9096   9101  9107   9112   9118  9123   9128   9134  35 

55  T.9134  T.9139  T.9144  T.9149  T.9155  ".9160  ".9165  ".9170  ".9175  ".9181  ".9186  34 

56  9186   9191   9196  9201   9206  9211   9216   9221  9226   9231   9236  33  5 

57  9236   9241   9246  9251   9255  9260   926u   9270  9275   9279   9284  32 

58  9284   9289   9294  9298   9303  9308   9312   9317  9322   9326   9331  31 

59  9331   9335   9340  9344   9349  9353   9358   9S62  9367   9371   9375  30 

60  ".9375  ".9380  ".9384  ".9388  ".9393  ".9397  ".9401  ".9406  T.9410  ".9414  ".9418  29 

61  9418   9422   9427  9431   9435  9439   9443   9447  9451   9455   9459  28 

62  9459   9463   9467  9471   9475  9479   9483   9487  9491   9495   9499  27  * 

63  9499   9503   95o6  9510   9514  9518   9522   9525  9529   9533   9537  26 

64  9537   9540   9544  9548   9551  9555   9553   9562  9566   9569   9573  25 

65  T.9573  ".9576  ".9580  ".9583  ".9587  T.9590  ".9594  ".9597  ".9601  ".9604  ".9607  24 

66  9607   9611   9614  9617   9621  9624   9627   9631  9634   9637   9640  23 

67  9640   9643   9647  9650   9653  9656   9659   9662  9665   9669   9672  22 

68  9672   9675   9678  9681   9634  9687   9690   9693  9696   9699   9702  21  * 

69  9702   9704   9707  9710   9713  9716   9719   9722  9724   9727   9730  20 

70  ".9730  ".9733  ".9735  ".9738  ".9741  ".9743  ".9746  ".9749  ".9751  1.9754  ~9757  19 

71  9757   9759   9762  9764   9767  9770   9772   9775  9777   9780   9782  18 

72  9782   9785   9787  9789   9792  9794   9797   9799  9801   9804   9806  17 

73  9806   9808   9811  9813   9815  9817   9820   9S22  9824   9826   9828  16 

74  9828   9831   9833  9835   9837  9839   9841   9843  9845   9847   9849  15 

75  ".9849  ".9851  ".9853  ".9855  ".9857  ".9859  ".9861  ".9863  ".9865  ".9867  ".9869  14  8 

76  9869   9871   9873  9875   9876  9878   9980   9882  9884   9885   9887  13 

77  9887   9889   9891  9892   9894  9896   9897   9899  9901   9902   9904  12 

78  9904   9906   9907  9909   9910  9912   9913   9915  9916   9918   9919  11 

79  9919   9921   9922  9924   9925  9927   9928   9929  9931   9932   9934  10 

£0  ".9934  "9935  ".9936  ".9937  T.9939  ".9940  T.9941  F.9943  ~9944  ".9945  L9946   9 

81  9946   9947   9949  9950   9951  9952   9953   9954  9955   9956   9953   8 

82  9958   9959   9960  9961   9962  9963   9964   9965  9966   9967   9968   7  * 

83  9968   9968   9969  9970   9971  9972   9973   9974  9975   9975   9676   6 

84  9976   9977   9978  9978   9979  9980   9981   9981  9982   9983   9983   5 

85  ".9983  ".9984  "99»5  ".9985  ".9986  ".9987  ".9987  ".998S  "9988  ".9989  7.9989   4 

86  9989   9990   9990  9991   9991  9992   9992   9993  9993   9994   9994   3 

87  9994   9994   9995  9995   9996   9996   9996   9996  9997   9997   9997   2 

88  9997   9998   9998  9998   9998   9999   9999   9999  9999   9999   9999   1 
89°  9999   9999   0000  0000   0000   0000   0000   0000   0000   0000   0000   0°  ° 

Complement    .D      .8  .7  .6  .5      .4     .3  .2      .1  .0  Angle 
Logarithmic  Cosines. 


818  Natural  Tangents.  Table  5. 

Angle    «0     ,1     ,2     ,3     .4     .5     .6     .7     ,8     .9   Complement  IK, 

0°  0.0000  0017  0035  0052  0070  0087  0105  0122  0140  0157  0175  89° 

1  0175  0192  0209  0227  0244  0262  0279  0297  0314  0332  0349  88 

2  0349  0367  0384  0402  0419  0437  0454  0472  0489  0507  0524  87 

3  0524  0542  0559  0577  0594  0612  0629  0647  0664  0682  0699  86 

4  0699  0717  0734  0752  0769  0787  0805  0822  0840  0857  0875  85 

5  0.0875  0892  0910  0928  0945  0963  0981  0998  1016  1033  1051  84 

6  1051  1069  1086  1104  1122  1139  1157  1175  1192  1210  1228  83 

7  1228  1246  1263  1281  1299  1317  1334  1352  1370  1388  1405  82 

8  1405  1423  1441  1459  1477  1495  1512  1530  1548  1566  1584  81 

9  1584  1602  1620  1638  1655  1673  1691  1709  1727  1745  1763  80 

10  0.1763  1781  1799  1817  1835  1853  1871  1890  1908  1926  1944  79  » 

11  1944  1962  1980  1998  2016  2035  2053  2071  2089  2107  2126  78 

12  2126  2144  2162  2180  2199  2217  2235  2254  2272  2290  2309  77 

13  2309  2327  2345  2364  2382  2401  2419  2438  2456  2475  2493  76 

14  2493  2512  2530  2549  2568  2586  2605  2623  2642  2661  2679  75 

15  0.2679  2698  2717  2736  2754  2773  2792  2811  2830  2849  2867  74 

16  2867  2886  2905  2924  2943  2962  2981  3000  3019  3038  3057  73  u 

17  3057  3076  3096  3115  3134  3153  3172  3191  3211  3230  3249  72 

18  3249  3269  3288  3307  3327  3346  3365  3385  3404  3424  3443  71 

19  3443  3463  3482  3502  3522  3541  3561  3581  3600  3620  3640  70 

20  0.3640  3659  3679  3699  3719  3739  3759  3779  3799  3819  3839  69 

21  3839  3859  3879  3899  3919  3939  3959  3979  4000  4020  4040  68  » 

22  4040  4061  4081  4101  4122  4142  4163  4183  4204  4224  4245  67 

23  4245  4265  4286  4307  4327  4348  4369  4390  4411  4431  4452  66 

24  4452  4473  4494  4515  4536  4557  4578  4599  4621  4642  4663  65  " 

25  0.4663  4684  4706  4727  4748  4770  4791  4813  4834  4856  4877  64 

26  4877  4899  4921  4942  4964  4986  5008  5029  5051  5073  5095  63 

27  5095  5117  5139  5161  5184  5206  5228  5250  5272  5295  5317  62  22 

28  5317  5340  5362  5384  5407  5430  5452  5475  5498  5520  5543  61 

29  5543  5566  5589  5612  5635  5658  5681  5704  5727  5750  5774  60  23 

30  0.5774  5797  5820  5844  5867  5890  5914  5938  5961  5985  6009  59 

31  6009  6032  6056  6080  6104  6128  6152  6176  6200  6224  6249  58  2* 

32  6249  6273  6297  6322  6346  6371  6395  6420  6445  §469  6494  57 

33  6494  6519  6544  6569  6594  6619  6644  6669  6694  6720  6745  56  » 

34  6745  6771  6796  6822  6847  6873  6899  6924  6950  6976  7002  55 

35  0.7002  7028  7054  7080  7107  7133  7159  7186  7212  7239  7265  54  * 

36  7265  7292  7319  7346  7373  7400  7427  7454  7481  7508  7536  53  » 

37  7536  7563  7590  7618  7646  7673  7701  7729  7757  7785  7813  52  * 

38  7813  7841  7869  7898  7926  7954  7983  8012  8040  8069  8098  51  M 

39  8098  8127  8156  8185  8214  8243  8273  8302  8332  8361  8391  50  29 

40  0.8391  8421  8451  8481  8511  8541  8571  8601  8632  8662  8693  49  s* 

41  8693  8724  8754  8785  8816  8847  8878  8910  8941  8972  9004  48  M 

42  9004  9036  9067  9099  9131  9163  9195  9228  9260  9293  9325  47  M 

43  9325  9358  9391  9424  9457  9490  9523  9556  9590  9623  9657  46  M 
44°  9657  9691  9725  9759  9793  9827  9861  9896  9930  9965  1,0000  45°  S4 

Complement    *9     *8     ,7     ,6     *5     «4     43     ,2     *i     *o   Angle 
Natural  Cotangents. 


6.  Natural  Tangents.  819 

Angle.  4<>       ,f       »2        ,3       44       ,5       «6       «7       *8       ,9     o». 


50  1.1918  1.1960  1.2002  1.2045  1.2088  1.2131  1.2174  1.2218  1.2261  1.2305 

51  1.2349  1.2393  1.2437  1.2482  1  2527  1.2572  1.2617  1.2662  1.2708  1.2753  46 

52  1.2799  1.2846  1.2892  1.2938  1.2985  1.3032  1.3079  1.3127  1.3175  1.3222  47 

53  1.3270  1.3319  1.3367  1.3416  1.3465  1.3514 1.3564  1.3613  1.3663  1.3713  49 

54  1.3764 1.3814  1.3865  1.3916  U968  1.4019  1.4071  1.4124 1.4176  1.4229  58 

55  1.4281  1.4335  1.4388  1.4442  1.4496  1.4550  1.4605  1.4659  1.4715  1.4770  M 

56  1.4826  1.4882  1.4938  1.4994  1.5051 1.5108  1.5166  1.5224  1.5282  1.5340  57 

57  1.5399  1.5458  1.5517  1.5577  1.5637  1.5697  1.5757  1.5818  1.5880  1.5941  60 

58  1.6003  1.6066  1.6128  1.6191  1.6255  1.6319  1.6383  1.6447  1.6512  1.6577  64 

59  1.6643  1.6709  1.6775  1.6842  1.6909  1.6977  1.7045  1.7113  1.7182 1.7251  8( 

60  1.7321 1.7391  1.7461  1.7532  1.7603  1.7675  1.7747  1.7820  1.7893  1.7966  n 

61  1.8040  1.8115  1.8190  1.8265  1.8341  1.8418  1.8495  1.8572  1.8650  1  8728  " 

62  1.8807  1.8887  1.8967  1.9047  1.9128  1.9210  1.9292  1.9375  1.9458  1.9542  8a 

63  1.9626  1.9711 1.9797  1.9883  1.9970  2.0057  2.0145  2.0233  2.0323  2.0413  ** 

64  2.0503  2.0594  2.0686  2.0778  2.0872  2.0965  2.1060  2.1155  2.1251  2.1348  * 

65  2.145  2.154  2.164  2.174  2.184  2.194   2.204  2.215   2.225   2.236    10 

66  2.246   2.257   2.267   2.278   2.289   2.300   2.311    2.322   2.333   2.344 

67  2.356   2.367   2.379   2.391    2.402   2.414  2.426   2.438   2.450   2.463     18 


68 

2.475 

2.488 

2.500 

2.513 

2.526 

2.539 

2.552 

2.565 

2.578 

2.592 

18 

69 

2.605 

2.619 

2.633 

2.646 

2.660 

2.675 

2.689 

2.703 

2.718 

2.733 

U 

70 

2.747 

2.762 

2.778 

2.793 

2.808 

2.824 

2.840 

2.856 

2.872 

2.888 

19 

71 

2.904 

2.921 

2.937 

2.954 

2.971 

2.989 

3.006 

3.024 

3.042 

3.060 

17 

72 

3.078 

3.096 

3.115 

3.133 

3.152 

3.172 

3.191 

3.211 

3.230 

3.250 

19 

73 

3.271 

3.291 

3.312 

3.333 

3.354 

3.376 

3.398 

3.420 

3.442 

3.465 

aa 

74 

3.487 

3.511 

3.534 

3.558 

3.582 

3.606 

3.630 

3.655 

3.681 

3.706 

85 

75 

3.732 

3.758 

3.785 

3.812 

3.839 

3.867 

3.895 

3.923 

3.952 

3.981 

*8 

76 

4.011 

4.041 

4.071 

4.102 

4.134 

4.165 

4.198 

4.230 

4.264 

4.297 

82 

77 

4.331 

4.366 

4.402 

4,437 

4.474 

4.511 

4.548 

4.586 

4.625 

4.665 

87 

78 

4.705 

4.745 

4.787 

4.829 

4.872 

4.915 

4.959 

5.005 

5.050 

5.097 

44 

79 

5.145 

5.193 

5.242 

5.292 

5.343 

5.396 

5.449 

5.503 

5.558 

5614 

61 

80 

5.67 

5.73 

5.79 

5.85 

5.91 

5.98 

6.04 

6.11 

6.17 

6.24 

7 

81 

6.31 

6.39 

6.46 

6.54 

6.61 

6.69 

6.77 

6.85 

6.94 

7.03 

8 

82 

7.12 

7.21 

7.30 

7.40 

7.49 

7.60 

7.70 

7.81 

7.92 

8.03 

10 

83 

8.14 

8.26 

8.39 

8.51 

8.64 

8.78 

8.92 

9.06 

9.21 

9.36 

Id 

84 

9.51 

9.68 

9.84 

10.0 

10.2 

10.4 

10.6 

10.8 

11.0 

11.2 

85 

11.4 

11.7 

11.9 

12.2 

12.4 

12.7 

13.0 

13.3 

13.6 

14.0 

8 

86 

14.3 

14.7 

15.1 

15.5 

15.9 

16.3 

16.8 

17.3 

17.9 

18.5 

6 

87 

19.1 

19.7 

20.4 

21.2 

22.0 

22.9 

23.9 

24.9 

26.0 

27.3 

88 

28.6 

30.1 

31.8 

33.7 

35.8 

382 

40.9 

441 

47.7 

52.1 

89°  57. 

64. 

72. 

82. 

95. 

115. 

143. 

191. 

286. 

573. 

ingle.  ^O       a        ,2        .3        .4        45       46        47        *3 

Natural  Tangents. 


820  Logarithmic  Tangents.  fable  5.  A. 

Angle  .0     .1  .3  .3      .4  .5     .6     .7  .8      .»  Complement  on 

0°-<=>o  IT.2419  3.5429  3.7190  3.8439  3.9409  2~.0200  2.0870  2~.1450  2".1962  2~.2419  89°  — 

1  2".2419  2~.2833  2>.3211  2".3559  2~.3881  2".4181  2.4461  2.4725  2~.4973  if.5208  £.5431  88  — 

2  5431   5643  5S45  6038   6223  6401   6571   6736   6894   704*  7194  87  — 
7194   7337  7475  7609   7739  7865   7988   8107  8223   8336  8446  86  — 

4  8446   8554  8659  8762   8362  8960   9056   9150  9241   9S31  9420  85  — 

5  JT.9420  2*9506  2*9591  2~.9674  2*9756  2*9836  2~.9915  2*9992  1*0068  :T.0143  T.0216  84  80 

6  f.0216  T.0289  ~.0360  T.0430  t.0499  ".0567  T.0633  T.0699  1*0764  T.0828  T.0891  83  68 

7  0891   0954  1015  1076   1135  1194   1252   1310   1367   1423  1478  82  59 
1478   1533  1587  1640   1693  1745   1797   1848  1898   1948  1997  81  M 

9   1997   2046  2094  2142   2189  2236   2282   2323  2374   2419  2463  80  48 

10  f.2643  1*.2507  ".2551  1*2594  f.2637  T.2680  f.2722  f.2764  7.2805  1*.2846  T.2887  79  4S 

11  2887   2927  2967  3006   3046  3085   3123   3162   3200   8237  8275  78  31 

12  S275   3312  8349  3385   3422  3453   3493   3529   3564   8599  3634  77  3 

13  3634   8668  8702  3736   8770  8804   3837   8870   8903   3935  8968  76  38 

14  8968   4000  4032  4064   4095  4127   4158   4189   4220   4250  4281  75  S1 

15  T.4281  T.4311  r.4341  5T.4371  7.4400  f.4430  f.4459  T*.4488  T.4517  f.4546  7.4575  74  29 

16  4575   4603  4632  4660   4633  4716   4744   4771   4799   4826  4853  73  2I 

17  4853   4880  4907  4934   4961  4987   5014   5040   5066   5092  5118  72  27 

18  5118   5143  5169  5195   5220  5245   5270   5295   5320   5345  5370  71  2* 

19  5370   5394  5419  5443   5467  5491   5516   5539   5563   6587  5611  70  24 

20  7.5611  7.5634  7.5658  7.5681  f.5704  f.5727  f.5750  l".5773  f,5796  T.5819  1*5842  69  28 

21  5342   5364  5887  5909   5932  5954   5976   5993   6020   6042  6064  68  2! 

22  6064   6086  6103  6129   6151  6172   6194   6215   6236   6257  6279  67  2 

23  6279   6300  6321  6341   6362  6383   6404   6424   6445   6465  6486  66  2 

24  6486   6506  6527  6547   6567  6587   6607   6627   6647   6667  6687  65  20 

25  F.6687  T".6706  f.6726  7.6746  f.6765  1*6785  T.6804  1*6824  7.6848  T.6863  1*.6882  64 

26  6882   6901  6920  6939   6958  6977   6996   7015   7034   7053  7072  63  W 

27  7072   7090  7109  7128   7146  7165   7183   7202   7220   7238  7257  62 

28  7257   7275  7293  7311   7330  7348   7366   7384   7402   7420  7438  61  l* 

29  7438   7455  7473  7491   7509  7526   7544   7562   7579   7597  7614  60 

30  1*.7614  F.7632  L7649  1*.7667  f.7684  T.7701  T.7719  T*.7736  T.7753  f.7771  l".7788  59 

31  7788   7805  7822  7839   7856  7873   7890   7907   7924   7941  7958  58  17 

32  7958   7975  7992  8008   8025  8042   8059   8075   8092   8109  8125  57 

33  8125   8142  8158  8175   8191  8203   8224   8241   8257   8274  8290  56 

34  8290   8306  8323  8339   8355  <*371   838S   8404   8420   8436  8452  55 

35  t.8452  l".8468  T.8484  T.8501  T.8517  T.8533  1*8549  T*.8565  T.8581  1*8597  T.8613  54  W 

8613   8629  8644  8660   8676  8692   8708   8724   8740   8755  8771  53 

37  8771   8787  8803  8818   8834  8350   8865   8881   8897   8912  8928  52 

38  8928   8944  8959  8975   8990  9006   9022   9037   9053   9068  9084  51 

39  9084   9099  9115  9130   9146  9161   9176   9192   9207   9223  9238  50 

40  f.9238  f.9254  lT.9269  t.9284  l".9300  9".9315  T*.9330  t.9346  T.9361  1^9376  T.9392  49 

41  9392   9407  9422  9438   9453  9468   9483   9499  9514   9529  9544  48 

42  9544   9560  9575  9590   9605  9621   9636  9651  9666   9681  9697  47 

43  9697   9712  9727  9742   9757  9772   9788   9803  9S18   9833  9843  46 
44°  9848   9864  9879  9894   9909  9924   9939   9955  9970   9985  0000  45°  1J 

Complement    .9  .8  .7      .6  .5      .4     .3      .2      .1  .0   Angle 

Logarithmic  Cotangents. 


table  5.  A.  Logarithmic  Tangents.  821 

Angle  .0     .1      .2  .3  .4  .5      .6  .7     .8  .•  Complement  on. 

45°  0.0000  0.0015  0.0030  0.0045  0.0061  0.0076  0.0091  0.0106  0.0121  0.0136  0.0152  44°  1§ 

46  0152   0167   0182  0197  0212  0223   0243  0258   0273  0288  0303  43 

47  OS03   0319   0334  0349  0364  0379   0395  0410   0425  0*40  0456  42 

48  0456   0471   0486  0501  0517  0532   0547  0562   057$  0593  0608  41 

49  OG08   0624   0639  0654  0670  0685   0700  0716   0731  0716  0762  40 

50  0.0762  0.0777  0.0793  0.0808  0.0824  0.0839  0.0854  0.0870  0.0885  0.090J  0.0916  39 

51  0916   0932   0947  0963  0978  0994   1010  1025   1041  1056  1072  38 

52  1072   1088   1103  1119  1135  1150   1166  1182   1197  1213  1229  37 

53  1229   1245   1260  127C  1292  1308   1324  1340   1356  J371  1387  36 

54  1387   1403   1419  1435  1451  1467   1483  1499   1516  1532  1548  35  19 

55  0.1548  0.1564  0.1580  0.1596  0.1612  0.1629  0.1645  0.1661  0.1677  0.1694  0.1710  34 

56  1710   1726   1743  1759  1776  1792   1809  1825   1842  1858  1875  33 

57  1875   1891   1908  1925  1941  1958   1975  1992   2008  2025  2042  32 

58  2042   2059   2076  2093  2110  2127   2144  2161   2178  2195  2212  31  tT 

59  2212   2229   2247  2264  2281  2299   2316  2333   2351  2368  2386  30 

60  0.2386  0.2403  0.2421  0.2438  0.2456  0.2474  0.2491  0.2509  0.2527  0.2545  0-2562  29 

61  2562   2580   2598  2616  2634  2652   2670  2689   2707  2725  2743  28  * 

62  2743   2762   2780  2798  2817  2835   2854  2872   2891  2910  2928  27 

63  2928   2947   2966  2985  3004  3023   3042  3061   3080  3099  3118  26  ** 

64  3118   3137   8157  Sl76  3196  3215   3235  3254   3274  3294  3313  25 

65  0.3313  0.3333  0.3353  0.3373  0.3393  0.3413  0.3433  0.3453  0.3473  0.3494  0.3514  24  8( 

66  3514   3535   3555  3576  8596  3617   3638  3659   3679  .'.  3700  8721  23  2 

67  3721   3743   3764  8785  3806  3828   3849  3871   3892  3914  8936  22  2: 

68  3936   3958   3980  4002  4024  4046   4068  4091   4113  4136  4158  21  2 

69  4158   4181   4204  4227  4250  4273   4296  4319   4342  4366  4389  20  2?' 

70  0.4389  0.4413  0.4437  0.4461  0.4484  0.4509  0.4533  0.4557  0.4581  0.4606  0.4630  19  2l 

71  4630   4655   4680  4705  4730  4755   4780  4805   4831  4857  4882  18  2! 

72  4882   4908   4934  4960  4986  5013   5039  5066   5093  5120  5147  17  2 

73  5147   5174   5201  5229  5256  5284   5312  5340   5368  5397  5425  16  2) 

74  5425   5454   5483  5512  5541  5570   5600  5629   5659  ,5689  5719  15  29 

75  0.5719  0.5750  0.5780  0.5811  0.5342  0.5873  0.5905  0.5936  0.5968  0.6000  0.6032  14  3^ 

76  6032   G065   6097  6130  6163  6196   6230   6264   6298  6332  6366  13  8 

77  6366   6401   6436  6471  6507  6542   6578  6615   6651  6688  6725  12  3( 

78  6725   G763   6800  6838  6877  6915   6954  6994   7033  7073  7113  11  S 

79  7113   7154   7195  7236  7278  7320   7363  7406   7449  7493  7537  10  4* 

80  0.7537  0.7581  0.7626  0.7672  0.7718  0.7764  0.7811  0.7858  0.7906  0.7954  0.8003  9  *' 

81  8003   8052   8102  8152  8203  8255   8307  8360   8413  8467  8522  8  8* 

82  8522   8577   8633  8690  8748  8806   8865  8924   8985  9046  9109  7  8 

83  9109   9172   9236  9301  9367  9433   9501  9570   9640  9711  9784  6  6! 

84  9734   9857   9932  1.0008  1.0085  1.0164  1  0244  1.0326  1.0409  1.0494  1.0580  5  *° 

85  1.0580  1.0669  1.0759  1.0850  1.0944  1.1040  1.1138  1.1238  1.1341  1.1446  1.1554  4  — 

86  1554   1664   1777  1893  2012  2135   2261  2391   2525  2663  2806  3  — 

87  2806   2954   3106  3264  3429  3599   3777  3962   4155  4357  4569  2  — 

88  4569   4792   5027  5275  5539  5819   6119  6441   6789  7167  7581  1  — 
89°  7581   8038   8553  9130  9800  2.0591  2.1561  2.2810  2.4571  2.7581  oo  0°  — 

Complement    .9     .8  .7  .6  .5      .4  .3      .2  .1  .0  Angle 
Logarithmic  Cotangents. 


.821a  Antilogarithras.  Table  5  (B). 

JLogs.  O  1    2  3  4    5    6    7  8  9  Dif. 

.00  1000  1002  1005  1007  1009  1012  1014  1016  1019  1021 

.01  1023  1026  1028  1030  1033  1035  1038  1040  1042  1045 

.02  1047  1050  1052  1054  1057  1059  1062  1064  1067  1069 

.03  1072  1074  1076  1079  1081  1084  1086  1089  1091  1094 

.04  1096  1099  1102  1104  1107  1109  1112  1114  1117  1119 

.05  1122  1125  1127  1130  1132  1135  1138  1140  1143  1146 

.06  1148  1151  1153  1156  1159  1161  1164  1167  1169  1172 

.07  1175  1178  1180  1183  1186  1189  1191  1194  1197  1199 

.08  1202  1205  1208  1211  1213  1216  1219  1222  1225  1227 

.09  1230  1233  1236  1239  1242  1245  1247  1250  1253  12F>6 

.10  1259  1262  1265  1268  1271  1274  1276  1279  1282  1285 

.11  1288  1291  1294  1297  1300  1303  1306  1309  1312  1315 

.12  1318  1321  1324  1327  1330  1334  1337  1340  1343  1346   3 

.13  1349  1352  1355  1358  1361  1365  1368  1371  1374  1377 

.14  1380  1384  1387  1390  1393  1396  1400  1403  1406  1409 

.15  1413  1416  1419  1422  1426  1429  1432  1435  1439  1442 

.16  1445  1449  1452  1455  1459  1462  1466  1469  1472  1476 

.17  1479  1483  1486  1489  1493  1496  1500  1503  1507  1510 

.18  1514  1517  1521  1524  1528  1531  1535  1538  1542  1545 

.19  1549  1552  1556  1560  1563  1567  1570  1574  1578  1581 

.20  1585  1589  1592  1596  1600  1603  1607  1611  1614  1618 

.21  1622  1626  1629  1633  1637  1641  1644  1648  1652  1656 

.22  1660  1663  1667  1671  1675  1679  1683  1687  1690  1694 

.23  1698  1702  1706  -  1710  1714  1718  1722  1726  1730  1734 

.24  1738  1742  1746  1750  1754  1758  1762  1766  1770  1774   4 

.25  1778  1782  1786  1791  1795  1799  1803  1807  1811  1816 

.26  1820  1824  1828  1832  1837  1841  1845  1849  1854  1858 

.27  1862  1866  1871  1875  1879  1884  1888  1892  1897  1901 

.28  1905  1910  1914  1919  1923  1928  1932  1936  1941  1945 

.29  1950  1954  1959  1963  1968  1972  1977  1982  1986  1991 

.30  1995  2000  2004  2009  2014  2018  2023  2028  2032  2037 

.31  2042  2046  2051  2056  2061  2065  2070  2075  2080  2084 

.32  2089  2094  2099  2104  2109  2113  2118  2123  2128  2133 

.33  2138  2143  2148  2153  2158  2163  2168  2173  2178  2183   5 

-34  2188  2193  2198  2203  2208  2213  2218  2223  2228  2234 

.35  2239  2244  2249  2254  2259  2265  2270  2275  2280  2286 

.36  2291  2296  2301  2307  2312  2317  2323  2328  2333  2339 

.37  2344  2350  2355  2360  2366  2371  2377  2382  2388  2393 

.38  2399  2404  2410  2415  2421  2427  2432  2438  2443  2449 

,39  2455  2460  2466  2472  2477  2483  2489  2495  2500  2506 

.40  2512  2518  2523  2529  2535  2541  2547  2553  2559  2564 

.41  2570  2576  2582  2588  2594  2600  2606  2612  2618  2624   6 

.42  2630  2636  2642  2649  2655  2661  2667  2673  2679  2685 

,43  2692  2698  2704  2710  2716  2723  2729  2735  2742  2748 

.44  2754  2761  2767  2773  2780  2786  2793  2799  2805  2812 

.45  2818  2825  2831  2838  2844  2851  2858  2864  2871  2877 

.46  2884  2891  2897  2904  2911  2917  2924  2931  2938  2944 

.47  2951  2958  2965  2972  2979  2985  2992  2999  3006  3013 

.48  3020  3027  3034  3041  3048  3055  3062  3069  3076  3083   7 

,49  3090  3097  3105  3112  3119  3126  3133  3141  3148  3155 


Table  5  (B).  Antilogarithms.  8216 

Logs.  O    1  2  3  4  5  6  7  8  9  Dif. 

.50  3162  3170  3177  3184  3192  3199  3206  3214  3221  3228 

.51  3236  3243  3251  3258  3266  3273  3281  3289  3296  3304 

.53  3311  3319  3327  3334  3342  3350  3357  3365  3373  3381 

.53  3388  3396  3404  3412  3420  3428  3436  3443  3451  3459   8 

.54  3467  3475  3483  3491  3499  3508  3516  3524  3532  3540 

.55  3548  3556  3565  3573  3581  3589  3597  3606  3614  3622 

.56  3631  3639  3648  .3656  3664  3673  3681  3690  3698  3707 

.57  3715  3724  3733  3741  3750  3758  3767  3776  3784  3793 

.58  3802  3811  3819  3828  3837  3846  3855  3864  3873  3882 

.59  3890  3899  3908  3917  3926  3936  3945  3954  3963  3972   9 

.60  3981  3990  3999  4009  4018  4027  4036  4046  4055  4064 

.61  4074  4083  4093  4102  4111  4121  4130  4140  4150  4159 

.63  4169  4178  4188  4198  4207  4217  4227  4236  4246  4256 

.t>3  4266  4276  4285  4295  4305  4315  4325  4335  4345  4355  10 

.64  4365  4375  4385  4395  4406  4416  4426  4436  4446  4457 

.65  4467  4477  4487  4498  4508  4519  4529  4539  4550  4560 

.66  4571  4581  4592  4603  4613  4624  4634  4645  4656  4667 

.67  4677  4688  4699  4710  4721  4732  4742  4753  4764  4775  11 

.68  4786  4797  4808  4819  4831  4842  4853  4864  4875  4887 

.69  4898  4909  4920  4932  4943  4955  4966  4977  4989  5000 

.70  5012  5023  5035  5047  5058  5070  5082  5093  5105  5117 

.71  5129  5140  5152  5164  5176  5188  5200  5212  5224  5236  12 

•72  5248  5260  5272  5284  5297  5309  5321  5333  5346  5358 

.73  5370  5383  5395  5408  5420  5433  5445  5458  5470  5483 

.74  5495  5508  5521  5534  5546  5559  5572  5585  5598  5610 

.75  5623  5636  5649  5662  5675  5689  5702  5715  5728  5741  13 

.76  5754  5768  5781  5794  5808  5821  5834  5848  5861  5875 

.77  5888  5902  5916  5929  5943  5957  5970  5984  5998  6012 

.78  6026  6039  6053  6067  6081  6095  6109  6124  6138  6152  14 

.79  6166  6180  6194  6209  6223  6237  6252  6266  6281  6295 

.80  6310  6324  6339  6353  6368  6383  6397  6412  6427  6442 

.81  6457  6471  6486  6501  6516  6531  6546  6561  6577  6592  15 

.82  6607  6622  6637  6653  6668  6683  6699  6714  6730  6745 

.83  6761  6776  6792  6808  6823  6839  6855  6871  6887  6902 

•84  6918  6934  6950  6966  6982  6998  7015  7031  7047  7063  16 

.85  7079  7096  7112  7129  7145  7161  7178  7194  7211  7228 

.86  7244  7261  7278  7295  7311  7328  7345  7362  7379  7396  17 

•8T  7413  7430  7447  7464  7482  7499  7516  7534  7551  7568 

.88  7586  7603  7621  7638  7656  7674  7691  7709  7727  7745 

.89  7762  7780  7798  7816  7834  7852  7870  7889  7907  7925  18 

.90  7943  7962  7980  7998  8017  8035  8054  8072  8091  8110 

.91  8128  8147'  8166  8185  8204  8222  8241  8260  8279  8299  19 

.92  8318  8337  8356  8375  8395  8414  8433  8453  8472  8492 

.93  8511  8531  8551  8570  8590  8610  8630  8650  8670  8690 

.94  8710  8730  8750  8770  8790  8810  8831  8851  8872  8892  20 

.95  8913  8933  8954  8974  8995  9016  9036  9057  9078  9099  21 

.96  9120  9141  9162  9183  9204  922^  9247  9268  9290  9311  21 

•97  9333  9354  9376  9397  9419  9441  9462  9484  9506  9528  22 

•98  9550  9572  9594  9616  9638  9661  9683  9705  9727  9750  22 

.99  9772  9795  9817  9840  9863  9886  9908  9931  9954  9977  23 


821<?  Pour-place  Logarithms.  Table  5  co. 

Nos.  O         1  2  3  4  5  6          7  8  9     Dif. 

10  0000  0043  0086  0128  0170  0212  0253  0294  0334  0374  42 

11  0414  0453  0492  0531  0569  0607  0645  0682  0719  0755  38 

12  0792  0828  0864  0899  0934  0969  1004  1038  1072  1106  35 

13  1139  1173  1206  1239  1271  1303  1335  1367  1399  1430  32 

14  1461  1492  1523  1553  1584  1614  1644  1673 %  1703  1732  30 

15  1761  1790  1818  1847  1875  1903  1931  1959  1987  2014  28 

16  2041  2068  2095  2122  2148  2175  2201  2227  2253  2279  26 

17  2304  2330  2355  2380  2405  2430  2455  2480  2504  2529  25 

18  2553  2577  2601  2625  2648  2672  2695  2718  2742  2765  23 

19  2788  2810  2833  2856  2878  2900  2923  2945  2967  2989  22 

20  3010  3032  3054  3075  3096  3118  3139  3160  3181  3201  21 

21  3222  3243  3263  3284  3304  3324  3345  3365  3385  3404  20 

22  3424  3444  3464  3483  3502  3522  3541  3560  3579  3598  .  19 

23  3617  3636  3655  3674  3692  3711  3729  3747  3766  3784  18 

24  3802  3820  3838  3856  3874  3892  3909  3927  3945  3962  18 

25  3979  3997  4014  4031  4048  4065  4082  4099  4116  4133  17 

26  4150  4166  4183  4200  4216  4232  4249  4265  4281  4298  16 

27  4314  4330  4346  4362  4378  4393  4409  4425  4440  4456  16 

28  4472  4487  4502  4518  4533  4548  4564  4579  4594  4609  15 

29  4624  4639  4654  4669  4683  4698  4713  4728  4742  4757  15 

30  4771  4786  4800  4814  4829  4843  4857  4871  4886  4900  14 

31  4914  4928  4942  4955  4969  4983  4997  5011  5024  5038 

32  5051  5065  5079  5092  5105  5119  5132  5145  5159  5172 

33  5185  5198  5211  5224  5237  5250  5263  5276  5289  5302  13 

34  5315  5328  5340  5353  5366  5378  5391  5403  5416  5428 

35  5441  5453  5465  5478  5490  5502  5514  5527  5539  5551 

36  5563  5575  5587  5599  5611  5623  5635  5647  5658  5670  12 

37  5682  5694  5705  5717  5729  5740  5752  5763  5775  5786 

38  5798  5809  5821  5832  5843  5855  5866  5877  5888  5899 

39  5911  5922  5933  5944  5955  5966  5977  5988  5999  6010  11 

40  6021  6031  6042  6053  6064  6075  6085  6096  6107  6117 

41  6128  6138  6149  6160  6170  6180  6191  6201  6212  6222 

42  6232  6243  6253  6263  6274  6284  6294  6304  6314  6325 

43  6335  6345  6355  6365  6375  6385  6395  6405  6415  6425  10 

44  6435  6444  6454  6464  6474  6484  6493  6503  6513  6522 

45  6532  6542  6551  6561  6571  6580  6590  6599  6609  6618 

46  6628  6637  6646  6656  6665  6675  6684  6693  6702  6712 

47  6721  6730  6739  6749  6758  6767  6776  6785  6794  6803 

48  6812  6821  6830  6839  6848  6857  6866  6875  6884  6893   9 

49  6902  6911  6920  6928  6937  6946  6955  6964  6972  6981 

50  6990  6998  7007  7016  7024  7033  7042  7050  7059  7067 

51  7076  7084  7093  7101  7110  7118  7126  7135  7143  7152 

52  7160  7168  7177  7185  7193  7202  7210  7218  7226  7235 

53  7243  7251  7259  7267  7275  7284  7292  7300  7308  7316 

54  7324  7332  7340  7348  7356  7364  7372  7380  7388  7396   8 


Table  5  (O.  Four-place  Logarithms. 

Nos.  O  1  2  3  4  5  6  7  8  9     Dif. 

55  7404  7412  7419  7427  7435  7443  7451  7459  7466  7474 

56  7482  7490  7497  7505  7513  7520  7528  7536  7543  7551 

57  7559  7566  7574  7582  7589  7597  7604  7612  7619  7627 

58  7634  7642  7649  7657  7664  7672  7679  7686  7694  7701 

59  7709  7716  7723  7731  7738  7745  7752  7760  7767  7774 

60  7782  7789  7796  7803  7810  7818  7825  7832  7839  7846 

61  7853  7860  7868  7875  7882  7889  7896  7903  7910  7917 

63  7924  7931  7938  7945  7952  7959  7966  7973  7980  7987   7 

63  7993  8000  8007  8014  8021  8028  8035  8041  8048  8055 

64  8062  8069  8075  8082  8089  8096  8102  8109  8116  8122 

65  8129  8136  8142  8149  8156  8162  8169  8176  8182  8189 

66  8195  8202  8209  8215  8222  8228  8235  8241  8248  8254 

67  8261  8267  8274  8280  8287  8293  8299  8306  8312  8319 

68  8325  8331  8338  8344  8351  8357  8363  8370  8376  8382 

69  8388  8395  8401  8407  8414  8420  8426  8432  8439  8445 

70  8451  8457  8463  8470  8476  8482  8488  8494  8500  8506 

71  8513  8519  8525  8531  8537  8543  8549  8555  8561  8567 

73  8573  8579  8585  8591  8597  8603  8609  8615  8621  8627   6 

73  8633  8639  8645  8651  8657  8663  8669  8675  8681  8686 

74  8692  8698  8704  8710  8716  8722  8727  8733  8739  8745 

75  8751  8756  8762  8768  8774  8779  8785  8791  8797  8802 

76  8808  8814  8820  8825  8831  8837  8842  8848  8854  8859 

77  8865  8871  8876  8882  8887  8893  8899  8904  8910  8915 

78  8921  8927  8932  8938  8943  8949  8954  8960  8965  8971 

79  8976  8982  8987  8993  8998  9004  9009  9015  9020  9025 

80  9031  9036  9042  9047  9053  9058  9063  9069  9074  9079 

81  9085  9090  9096  9101  9106  9112  9117  9122  9128  9133 
83  9138  9143  9149  9154  9159  9165  9170  9175  9180  9186 

83  9191  9196  9201  9206  9212  9217  9222  9227  9232  9238 

84  9243  9248  9253  9258  9263  9269  9274  9279  9284  9289 

85  9294  9299  9304  9309  9315  9320  9325  9330  9335  9340 

86  9345  9350  9355  9360  9365  9370  9375  9380  9385  9390 

87  9395  9400  9405  9410  9415  9420  9425  9430  9435  9440   5 

88  9445  9450  9455  9460  9465  9469  9474  9479  9484  9489 

89  9494  9499  9504  9509  9513  9518  9523  9528  9533  9538 

90  9542  9547  9552  9557  9562  9566  9571  9576  9581  9586 

91  9590  9595  9600  9605  9609  9614  9619  9624  9628  9633 

92  9638  9643  '  9647  9652  9657  9661  9666  9671  9675  9680 

93  9685  9689  9694  9699  9703  9708  9713  9717  9722  9727 

94  9731  9736  9741  9745  9750  9754  9759  9763  9768  9773 

95  9777  9782  9786  9791  9795  9800  9805  9809  9814  9818 

96  9823  9827  9832  9836  9841  9845  9850  9854  9859  9863 

97  9868  9872  9877  9881  9886  9890  9894  9899  9903  9908 

98  9912  9917  9921  9926  9930  9934  9939  9943  9948  9952 

99  9956  9961  9965  9969  9974  9978  9983  9987  9991  9996 


822  Logarithms.  Table  6. 

10.        0         I          2         3         4         5          6         7         8        9    on. 

100  00000  00043  00087  00130  00173  00217  00260  00303  00346  00389  ,434 

101  00432  00475  00518  00561  00604  00647  00689  00732  00775  00817  |  ,93 

102  00860  00903  00945  00988  01030  01072  01115  01157  01199  01242  * " 

103  01284  01326  01368  01410  01452  01494  01536  01578  01620  01662  67^« 

104  01703  01745  01787  01828  01870  01912  01953  01995  02036  02078  HI 

105  02119  02160  02202  02243  02284  02325  02366  02407  02449  02490  f\ 

106  02531  02572  02612  02653  02694  02735  02776  02816  02857  02898  i,| 

107  02938  02979  03019  03060  03100  03141  03181  03222  03262  03302  «»? 

108  03342  03383  03423  03463  03503  03543  03583  03623  03663  03703  • « 

109  03743  03782  03822  03862  03902  03941  03981  04021  04060  04100  §  |? 

110  04139  04179  04218  04258  04297  04336  04376  04415  04454  04493  ,394 

111  04532  04571  04610  04650  04689  04727  04766  04805  04844  04883  |,« 

112  04922  04961  04999  05038  05077  05115  05154  05192  05231  05269  « »• 

113  05308  05346  05385  05423  05461  05500  05538  05576  05614  05652  •  »? 

114  05690  05729  05767  05805  05843  05881  05918  05956  05994  06032  j" 

115  06070  06108  06145  06183  06221  06258  06296  06333  06371  06408  ,374 

116  06446  06483  06521  06558  06595  06633  06670  06707  06744  06781  J,J 

117  06819  06856  06893  06930  06967  07004  07041  07078  07115  07151  { }» 

118  07188  07225  07262  07298  07335  07372  07408  07445  07482  07518  •& 

119  07555  07591  07628  07664  07700  07737  07773  07809  07846  07882  ||o 

120  07918  07954  07990  08027  08063  08099  08135  08171  08207  08243  ,354 

121  08279  08314  08350  08386  08422  08458  08493  08529  08565  08600  I  ,? 

122  08636  08672  08707  08743  08778  08814  08849  08884  08920  08955  J  }* 

123  08991  09026  09061  09096  09132  09167  09202  09237  09272  09307  \% 

124  09342  09377  09412  09447  09482  09517  09552  09587  09621  09656  §  ft 

125  09691  09726  09760  09795  09830  09864  09899  09934  09968  10003  *\ 

126  10037  10072  10106  10140  10175  10209  10243  10278  10312  10346  32io 

127  10380  10415  10449  10483  10517  10551  10585  10619  10653  10687  $}$ 

128  10721  10755  10789  10823  10857  10890  10924  10958  10992  11025  •$ 

129  11059  11093  11126  11160  11193  11227  11261  11294  11327  11361  $1] 

130  11394  11428  11461  11494  11528  11561  11594  11628  11661  11694  ft 

131  11727  11760  11793  11826  11860  11893  11926  11959  11992  12024  1,1 


134  12710  12743  12775  12808  12840  12872  12905  12937  12969  13001 

135  13033  13066  13098  13130  13162  13194  13226  13258  13290  13322  ft 

136  13354  13386  13418  13450  13481  13513  13545  13577  13609  13640  §,• 

137  13672  13704  13735  13767  13799  13830  13862  13893  13925  13956  J  }| 

138  13988  14019  14051  14082  14114  14145  14176  14208  14239  14270  « J2 

139  14301  14333  14364  14395  14426  14457  14489  14520  14551  14582  gfS 

140  14613  14644  14675  14706  14737  14768  14799  14829  14860  14891  ?\ 

141  14922  14953  14983  15014  15045  15076  15106  15137  15168  15198  1  « 

142  15229  15259  15290  15320  15351  15381  15412  15442  15473  15503  $\t 

143  15534  15564  15594  15625  15655  15685  15715  15746  15776  15806  •  J? 

144  15836  15866  15897  15927  15957  15987  16017  16047  16077  16107  g |» 

145  16137  16167  16197  16227  16256  16286  16316  16346  16376  16406  ft 

146  16435  16465  16495  16524  16554  16584  16613  16643  16673  16702  J  g 

147  16732  16761  16791  16820  16850  16879  16909  16938  16967  16997  JJg 

148  17026  17056  17085  17114  17143  17173  17202  17231  17260  17289  ?JJ 

149  17319  17348  17377  17406  17435  17464  17493  17522  17551  17580  gf* 

150  17609  17638  17667  17696  17725  17754  17782  17811  17840  17869 


fable  6.  Logarithms.  823 

NO,   0123456789   oif. 

150  17609  17638  17667  17696  17725  17754  17782  17811  17840  17869  ,293 

151  17898  17926  17955  17984  18013  18041  18070  18099  18127  18156  g  f 

152  18184  18213  18241  18270  18298  18327  18355  18384  18412  18441  * JJ 

153  18469  18498  18526  18554  18583  18611  18639  18667  18696  18724  $ » 

154  18752  18780  18808  18837  18865  18893  18921  18949  18977  19005  j{  H 

155  19033  19061  19089  19117  19145  19173  19201  19229  19257  19285  ,288 

156  19312  19340  19368  19396  19424  19451  19479  19507  19535  19562  f  • 

157  19590  19618  19645  19673  19700  19728  19756  19783  19811  19838  *» 

158  19866  19893  19921  19948  19976  20003  20030  20058  20085  20112  •" 

159  20140  20167  20194  20222  20249  20276  20303  20330  20358  20385  • g 

160  20412  20439  20466  20493  20520  20548  20575  20602  20629  20656  ,278 

161  20683  20710  20737  20763  20790  20817  20844  20871  20898  20925  }  I 

162  20952  20978  21005  21032  21059  21085  21112  21139  21165  21192  JJJ 

163  21219  21245  21272  21299  21325  21352  21378  21405  21431  21458  • if 

164  21484  21511*21537  21564  21590  21617  21643  21669  21696  21722  « « 

165  21748  21775  21801  21827  21854  21880  21906  21932  21958  21985  ,268 

166  22011  22037  22063  22089  22115  22141  22167  22194  22220  22246  1  * 

167  22272  22298  22324  22350  22376  22401  22427  22453  22479  22505  *J§ 

168  22531  22557  22583  22608  22634  22660  22686  22712  22737  22763  °}« 

169  22789  22814  22840  22866  22891  22917  22943  22968  22994  23019  |.« 

170  23045  23070  23096  23121  23147  23172  23198  23223  23249  23274  ,258 

171  23300  23325  23350  23376  23401  23426  23452  23477  23502  23528  f  | 

172  23553  23578  23603  23629  23654  23679  23704  23729  23754  23779  «}• 

173  23805  23830  23855  23880  23905  23930  23955  23980  24005  24030  67  {* 

174  24055  24080  24105  24130  24155  24180  24204  24229  24254  24279  «g 

175  24304  24329  24353  24378  24403  24428  24452  24477  24502  24527 

176  24551  24576  24601  24625  24650  24674  24699  24724  24748  24773 

177  24797  24822  24846  24871  24895  24920  24944  24969  24993  25018 

178  25042  25066  25091  25115  25139  25164  25188  25212  25237  25261 

179  25285  25310  25334  25358  25382  25406  25431  25455  25479  25503 

180  25527  25551  25575  25600  25624  25648  25672  25696  25720  25744  ,a*2 

181  25768  25792  25816  25840  25864  25888  25912  25935  25959  25983  |  * 

182  20007  26031  26055  26079  26102  26126  26150  26174  26198  26221  *}» 

183  26245  26269  26293  26316  26340  26364  26387  26411  26435  26458  «{« 

184  26482  26505  26529  26553  26576  26600  26623  26647  26670  26694  g|» 

185  26717  26741  26764  26788  26811  26834  26858  26881  26905  26928  ?\ 

186  26951  26975  26998  27021  27045  27068  27091  27114  27138  27101  1  * 

187  27184  27207  27231  27254  27277  27300  27323  27346  27370  27303  \  • 

188  27416  27439  27462  27485  27508  27531  27554  27577  27600  27623  67  }$ 

189  27646  27669  27692  27715  27738  27761  27784  27807  27830  27852  | af 

190  27875  27898  27921  27944  27967  27989  28012  28035  28058  28081 

191  28103  28126  28149  28171  28194  28217  28240  28262  28285  28307 

192  28330  28353  28875  28398  28421  28443  28466  28488  28511  28533 

193  28556  28578  28601  28623  28646  28668  28691  28713  28735  28758 

194  28780  28803  28825  28847  28870  28892  28914  28937  28959  28981 

195  29003  29026  29048  29070  29092  29115  29137  29159  29181  29203  ,23a 

196  29226  29248  29270  29292  29314  29336  29358  29380  29403  29425  |  $ 

197  29447  29469  29491  29513  29535  29557  29579  29601  29623  29645  « ,? 

198  29667  29688  29710  29732  29754  29776  29798  29820  29842  29863  •  }| 

199  29885  29907  29929  29951  29973  29994  30016  30038  30060  30081  *& 
20030103  30125  30146.30168  30190  30211  30233  30255  30276  30298 


824  Logarithms.  Table  6. 

NO,   0    f    *    3    4    5    6    7    8    9  nit. 

200  30103  30125  30146  30168  30190  30211  30233  30255  30276  30298  21 

201  30320  30341  30363  30384  30406  30428  30449  30471  30492  30514 '  • 

202  30535  30557  30578  30600  30621  30643  30664  30685  30707  30728 2  * 

203  30750  30771  30792  30814  30835  30856  30878  30899  30920  30942 3  • 

204  30963  30984  31006  31027  31048  31069  31091  31112  31133  31154*  8 

205  31175  31197  31218  31239  31260  31281  31302  31323  31345  31366 5" 

206  31387  31408  31429  31450  31471  31492  31513  31534  31555  31576 6ia 

207  31597  31618  31639  31660  31681  31702  31723  31744  31765  31785 715 

208  31806  31827  31848  31869  31890  31911  31931  31952  31973  31994817 

209  32015  32035  32056  32077  32098  32118  32139  32160  32181  32201 9 » 

210  32222  32243  32263  32284  32305  32325  32346  32366  32387  32408  20 

211  32428  32449  32469  32490  32510  32531  32552  32572  32593  32613 »  • 

212  32634  32654  32675  32695  32715  32736  32756  32777  32797  32818 2  * 

213  32838  32858  32879  32899  32919  32940  32960  32980  33001  33021s  e 

214  33041  33062  33082  33102  33122  33143  33163  33183  33203  33224*  8 

215  33244  33264  33284  33304  33325  33345  33365  33385  33405  33425 5 10 

216  33445  33465  33486  33506  33526  33546  33566  33586  33606  33626 612 

217  33646  33666  33686  33706  33726  33746  33766  33786  33806  33826 7  » 

218  33846  33866  33885  33905  33925  33945  33965  33985  34005  34025 8 16 

219  34044  34064  34084  34104  34124  34143  34163  34183  34203  34223 ' 18 

220  34242  34262  34282  34301  34321  34341  34361  34380  34400  34420  i> 

221  34439  34459  34479  34498  34518  34537  34557  34577  34596  34616 »  a 

222  34635  34655  34674  34694  34713  34733  34753  34772  34792  3481 12  4 

223  34830  34850  34869  34889  34908  34928  34947  34967  34986  35005  s  fl 

224  35025  35044  35064  35083  35102  35122  35141  35160  35180  35199*  8 

225  35218  35238  35257  35276  35295  35315  35334  35353  35372  35392 51° 

226  35411  35430  35449  35468  35488  35507  35526  35545  35564  35583  •" 

227  35603  35622  35641  35660  35679  35698  35717  35736  35755  35774 71S 

228  35793  35813  35832  35851  35870  35889  35908  35927  35946  35965  81» 

229  35984  36003  36021  36040  36059  36078  36097  36116  36135  3615491T 

230  36173  36192  36211  36229  36248  36267  36286  36305  36324  38342 

231  36361  36380  36399  36418  36436  36455  36474  36493  36511  36530 

232  36549  36568  36586  36605  36624  36642  36661  36680  36698  36717 

233  36736  36754  36773  36791  36810  36829  36847  36866  36884  36903 

234  36922  36940  36959  36977  36996  37014  37033  37051  37070  37088 

235  37107  37125  37144  37162  37181  37199  37218  37236  37254  37273 

236  37291  37310  37328  37346  37365  37383  37401  37420  37438  37457 

237  37475  37493  37511  37530  37548  37566  37585  37603  37621  37639 

238  37658  37676  37694  37712  37731  37749  37767  37785  37803  37822 

239  37840  37858  37876  37894  37912  37931  37949  37967  37985  38003 

24038021  38039  38057  38075  38093  38112  38130  38148  38166  38184  w 
241  38202  38220  38238  38256  38274  38292  38310  38328  38346  38304  1  * 
24238382  38399  38417  38435  38453  38471  38489  38507  38525  38543s  * 
24338561  38578  38596  38614  38632  38650  38668  38686  38703  38721s  * 

244  38739  38757  38775  38792  38810  38828  38846  38863  38881  38899*  ' 

245  38917  38934  38952  38970  38987  39005  39023  39041  39058  39076 *  • 

246  39094  39111  39129  39146  39164  39182  39199  39217  39235  39252 6 " 

247  39270  39287  39305  39322  39340  39358  39375  39393  39410  39428  TW 
24839445  39463  39480  39498  39515  39533  39550  39568  39585  39602 81* 

249  39620  39637  39655  39672  39690  39707  39724  39742  39759  39777  9  lfl 

250  39794  39811  39829  39846  39863  39881  39898  39915  39933  39950 


Table  6.  Logarithms.  825 


NO.   0    1    2    3    4    5    6    7    8    9   oif. 

250  39794  39811  39829  39846  39863  39881  39898  39915  39983  39950  « 

251  39967  39985  40002  40019  40037  40054  40071  40088  40106  40123  l  2 

252  40140  40157  40175  40192  40209  40226  40243  40261  40278  40295  2  3 

253  40312  40329  40346  40364  40381  40398  40415  40432  40449  40466  3  5 

254  40483  40500  40518  40535  40552  40569  40586  40603  40620  40637  4  7 

255  40654  40671  40688  40705  40722  40739  40756  40773  40790  40807  B  9 

256  40824  40841  40858  40875  40892  40909  40926  40943  40960  40976  6 10 

257  40993  41010  41027  41044  41061  41078  41095  41111  41128  41145  7 12 

258  41162  41179  41196  41212  41229  41246  41263  41280  41296  41313  8 14 

259  41330  41347  41363  41380  41397  41414  41430  41447  41464  41481  9 15 

260  41497  41514  41531  41547  41564  41581  41597  41614  41631  41647 
2IM  41664  41681  41697  41714  41731  41747  41764  41780  41797  41814 
2(52  41830  41847  41863  41880  41896  41913  41929  41946  41963  41979 
203  41996  42012  42029  42045  42062  42078  42095  42111  42127  42144 

264  42160  42177  42193  42210  42226  42243  42259  42275  42292  42308 

265  42325  42341  42357  42374  42390  42406  42423  42439  42455  42472 

266  42488  42504  42521  42537  42553  42570  42586  42602  42619  42635 

267  42651  42667  42684  42700  42716  42732  42749  42765  42781  42797 

268  42813  42830  42846  42862  42878  42894  42911  42927  42943  42959 

269  42975  42991  43008  43024  43040  43056  43072  43088  43104  43120 

270  43136  43152  43169  43185  43201  43217  43233  43249  43265  43281  i« 

271  43297  43313  43329  43345  43361  43377  43393  43409  43425  43441  »  • 

272  43457  43473  43489  43505  43521  43537  43553  43569  43584  43600  2  8 

273  43616  43632  43648  43664  43680  43696  43712  43727  43743  43759 

274  43775  43791  43807  43823  43838  43854  43870  43886  43902  43917 

275  43933  43949  43965  43981  43996  44012  44028  44044  44059  44075 

276  44091  44107  44122  44138  44154  44170  44185  44201  44217  44232 

277  44248  44264  44279  44295  44311  44326  44342  44358  44373  44389 

278  44404  44420  44436  44451  44467  44483  44498  44514  44529  44545  8 13 

279  44560  44576  44592  44607  44623  44638  44654  44669  44685  44700  9 " 

280  44716  44731  44747  44762  44778  44793  44809  44824  44840  44855 

281  44871  44886  44902  44917  44932  44948  44963  44979  44994  45010 

282  45025  45040  45056  45071  45086  45102  45117  45133  45148  45163 

283  45179  45194  45209  45225  45240  45255  45271  45286  45301  45317 

284  45332  45347  45362  45378  45393  45408  45423  45439  45454  45469 

285  45484  45500  45515  45530  45545  45561  45576  45591  45606  45621 

286  45637  45652  45667  45682  45697  45712  45728  45743  45758  45773 

287  45788  45803  45818  45834  45849  45864  45879  45894  45909  45924 

288  45939  45954  45969  45984  46000  46015  46030  46045  46060  46075 

289  46090  46105  46120  46135  46150  46165  46180  46195  46210  46225 

290  46240  46255  46270  46285  46300  46315  46330  46345  46359  46374  « 

291  46389  46404  46419  46434  46449  46464  46479  46494  46509  46523  l 

292  46538  46553  46568  46583  46598  46613  46627  46642  46657  46672 

293  46687  46702  46716  46731  46746  46761  46776  46790  46805  46820 

294  46835  46850  46864  46879  46894  46909  46923  46938  46953  46967 

295  46982  46997  47012  47026  47041  47056  47070  47085  47100  47114 

296  47129  47144  47159  47173  47188  47202  47217  47232  47246  47261 

297  47276  47290  47305  47319  47334  47349  47363  47378  47392  47407 

298  47422  47436  47451  47465  47480  47494  47509  47524  47538  47553  8 12 
S99  47567  47582  47596  47611  47625  47640  47654  47669  47683  47698  9 " 
300  47712  47727  47741  47756  47770  47784  47799  47813  47828  47842 


826  Logarithms.  Table  6. 

Id.     0         1         2         3         4         5         6         7         8         9       on. 

300  47712  47727  47741  47756  47770  47784  47799  47813  47828  47842  u 

301  47857  47871  47885  47900  47914  47929  47943  47958  47972  47986  l  l 

302  48001  48015  48029  48044  48058  48073  48087  48101  48116  48130 

303  48144  48159  48173  48187  48202  48216  48230  48244  48259  48273 

304  48287  48302  48316  48330  48344  48359  48373  48387  48401  48416 

305  48430  48444  48458  48473  48487  48501  48515  48530  48544  48558 

306  48572  48586  4S601  48615  48629  48643  48657  48671  48686  48700 

307  48714  48728  48742  48756  48770  48785  48799  48813  48827  48841 

308  48855  48869  48883  48897  48911  48926  48940  48954  48968  48982 

309  48996  49010  49024  49038  49052  49066  49080  49094  49108  49122 

310  49136  49150  49164  49178  49192  49206  49220  49234  49248  49262 

311  49276  49290  49304  49318  49332  49346  49360  49374  49388  49402 

312  49415  49429  49443  49457  49471  49485  49499  49513  49527  49541 

313  49554  49568  49582  49596  49610  49624  49638  49651  49665  49679 

314  49693  49707  49721  49734  49748  49762  49776  49790  49803  49817 

315  49831  49845  49859  49872  49886  49900  49914  49927  49941  49955 

316  49969  49982  49996  50010  50024  50037  50051  50065  50079  50092 

317  50106  50120  50133  50147  50161  50174  50188  50202  50215  50229 

318  50243  50256  50270  50284  50297  50311  50325  50338  50352  50365 

319  50379  50393  50406  50420  50433  50447  50461  50474  50488  50501 

320  50515  50529  50542  50556  50569  50583  50596  50610  50623  50637 

321  50651  50664  50678  50691  50705  50718  50732  50745  50759  50772 

322  50786  50799  50813  50826  50840  50853  50866  50880  50893  50907 

323  50920  50934  50947  50961  50974  50987  51001  51014  51028  51041 

324  51055  51068  51081  51095  51108  51121  51135  51148  51162  51175 

325  51188  51202  51215  51228  51242  51255  51268  51282  51295  51308 

326  51322  51335  51348  51362  51375  51388  51402  51415  51428  51441 

327  51455  51468  51481  51495  51508  51521  51534  51548  51561  51574 

328  51587  51601  51614  51627  51640  51654  51667  51680  51693  51706 

329  51720  51733  51746  51759  51772  51786  51799  51812  51825  51838 

330  51851  51865  51878  51891  51904  51917  51930  51943  51957  51970  is 

331  51983  51996  52009  52022  52035  52048  52061  52075  52088  52101  l  1 

332  52114  52127  52140  52153  52166  52179  52192  52205  52218  52231  2  8 

333  52244  52257  52270  52284  52297  52310  52323  52336  52349  52362 

334  52375  52388  52401  52414  52427  52440  52453  52466  52479  52492 

335  52504  52517  52530  52543  52556  52569  52582  52595  52608  52621 

336  52634  52647  52660  52673  52686  52699  52711  52724  52737  52750 

337  52763  52776  52789  52802  52815  52827  52840  52853  52866  52879 

338  52892  52905  52917  52930  52943  52956  52969  52982  52994  53007 

339  53020  53033  53046  53058  53071  53084  53097  53110  53122  53135  912 

340  53148  53161  53173  53186  53199  53212  53224  53237  53250  53263 

341  53275  53288  53301  53314  53326  53339  53352  53364  53377  53390 

342  53403  53415  53428  53441  53453  53466  53479  53491  53504  53517 

343  53529  53542  53555  53567  53580  53593  53605  53618  53631  53643 

344  53656  53668  53681  53694  53706  53719  53732  53744  53757  53769 

345  53782  53794  53807  53820  53832  53845  53857  53870  53882  53895 

346  53908  53920  53933  53945  53958  53970  53983  53995  54008  54020 

347  54033  54045  54058  54070  54083  54095  54108  54120  54133  54145 
848  54158  54170  54183  54195  54208  54220  54233  54245  54258  54270 
:$49  54283  54295  54307  54320  54332  54345  54357  54370  54382  54394 
350  54407  54419  54432  54444  54456  54469  54481  54494  54506  54518 


Table  6.  Logarithms.  827 

10.   0    1    2    8    4    5    6    7    8    9   oir 

350  54407  54419  54432  54444  54456  54469  54481  54494  54506  54518  12 

351  54531  54543  54555  54568  54580  54593  54605  54617  54630  54642  l 

352  54654  54667  54679  54691  54704  54716  54728  54741  54753  54765  2 

353  54777  54790  54802  54814  54827  54839  54851  54864  54876  54888  s 

354  54900  54913  54925  54937  54949  54962  54974  54986  54998  55011  * 

355  55023  55035  55047  55060  55072  55084  55096  55108  55121  55133  5 

356  55145  55157  55169  55182  55194  55206  55218  55230  55242  55255  6 

857  55267  55279  55291  55303  55315  55328  55340  55352  55364  55376  7 

858  55388  55400  55413  55425  55437  55449  55461  55473  55485  55497  8 » 

359  55509  55522  55534  55546  55558  55570  55582  55594  55606  55618  9U 

360  55630  55642  55654  55666  55678  55691  55703  55715  55727  55739 

361  55751  55763  55775  55787  55799  55811  55823  55835  55847  55859 

362  55871  55883  55895  55907  55919  55931  55943  55955  55967  55979 

363  55991  56003  56015  56027  56038  56050  56062  56074  56086  56098 

364  56110  56122  56134  56146  56158  56170  56182  56194  56205  56217 

365  56229  56241  56253  56265  56277  56289  56301  56312  56324  56336 

366  56348  56360  56372  56384  56396  56407  56419  56431  56443  56455 

367  56467  56478  56490  56502  56514  56526  56538  56549  56561  56573 

368  56585  56597  56608  56620  56632  56644  56656  56667  56679  56691 

369  56703  56714  56726  56738  56750  56761  56773  56785  56797  56808 

370  56820  56832  56844  56855  56867  56879  56891  56902  56914  56926 

371  56937  56949  56961  56972  56984  56996  57008  57019  57031  57043 

372  57054  57066  57078  57089  57101  57113  57124  57136  57148  57159 

373  57171  57183  57194  57206  57217  57229  57241  57252  57264  57276 

374  57287  57299  57310  57322  57334  57345  57357  57368  57380  57392 

375  57403  57415  57426  57438  57449  57461  57473  57484  57496  57507 

376  57519  57530  57542  57553  57565  57576  57588  57600  57611  57623 

377  57634  57646  57657  57669  57680  57692  57703  57715  57726  57738 

378  57749  57761  57772  57784  57795  57807  57818  57830  57841  57852 

379  57864  57875  57887  57898  57910  57921  57933  57944  57955  57967 

380  57978  57990  58001  58013  58024  58035  58047  58058  58070  58081 

381  58092  58104  58115  58127  58138  58149  58161  58172  58184  58195 

382  58206  58218  58229  58240  58252  58263  58274  58286  58297  58309 

383  58320  58331  58343  58354  58365  58377  58388  58399  58410  58422 

384  58433  58444  58456  58467  58478  58490  58501  58512  58524  58535 

385  58546  58557  58569  58580  58591  58602  58614  58625  58636  58647 

386  58659  58670  58681  58692  58704  58715  58726  58737  58749  58760 

387  58771  58782  58794  58805  58816  58827  58838  58850  58861  58872 
•388  58883  58894  58906  58917  58928  58939  58950  58961  58973  58984 

389  58995  59006  59017  59028  59040  59051  59062  59073  59084  59095 

390  59106  59118  59129  59140  59151  59162  59173  59184  59195  59207 

391  59218  59229  59£40  59251  59262  59273  59284  59295  59306  59318  l 

392  59329  59340  59351  59362  59373  59384  59395  59406  59417  59428  2 

393  59439  59450  59461  59472  59483  59494  59506  59517  59528  59539  3 

394  59550  59561  59572  59583  59594  59605  59616  59627  59638  59649  4 

895  59660  59671  59682  59693  59704  59715  59726  59737  59748  59759  5 

396  59770  59780  59791  59802  59813  59824  59835  59846  59857  59868  6 

397  59879  59890  59901  59912  59923  59934  59945  59956  59966  59977  7 

398  59988  59999  60010  60021  60032  60043  60054  60065  60076  60086  8 

399  60097  60108  60119  60130  60141  60152  60163  60173  60184  60195  9 

400  60206  60217  60228  60239  60249  60260  60271  60282  60293  60304 


828  Logarithms.  Table  6. 

JO,       0         1         2        3         4         5          6         7         8        9    oif. 

400  60206  60217  60228  60239  60249  60260  60271  60282  60293  60304  " 

401  60314  60325  60336  60347  60358^60369  60379  60390  60401  60412  l  * 

402  60423  60433  60444  60455  60466  60477  60487  60498  60509  60520  2  • 

403  60531  60541  60552  60563  60574  60584  60595  60606  60617  60627   « 

404  60638  60649  60660  60670  60681  60692  60703  60713  60724  60735  * 

405  60746  60756  60767  60778  60788  60799  60810  60821  60831  60842 
40(>  60853  60863  60874  60885  60895  60906  60917  60927  60938  60949 

407  60959  60970  60981  60991  61002  61013  61023  61034  61045  61055 

408  61066  61077  61087  61098  61109  61119  61130  61140  61151  61162 

409  61172  61183  61194  61204  61215  61225  61236  61247  61257  61268 

410  61278  61289  61300  61310  61321  61331  61342  61352  61363  61374 

411  61384  61395  61405  61416  61426  61437  61448  61458  61469  61479 

412  61490  61500  61511  61521  61532  61542  61553  61563  61574  61584 

413  61595  61606  61616  61627  61637  61648  61658  61669  61679  61690 

414  61700  61711  61721  61731  61742  61752  61763  61773  61784  61794 

415  61805  61815  61826  61836  61847  61857  61868  61878  61888  61899 

416  61909  61920  61930  61941  61951  619&2  61972  61982  61993  62003 

417  62014  62024  62034  62045  62055  62066  62076  62086  62097  62107 

418  62118  62128  62138  62149  62159  62170  62180  62190  62201  62211 

419  62221  62232  62242  62252  62263  62273  62284  62294  62304  62315 

420  62325  62335  62346  62356  62366  62377  62387  62397  62408  62418  10 

421  62428  62439  62449  62459  62469  62480  62490  62500  62511  62521  1  1 

422  62531  62542  62552  62562  62572  62583  62593  62603  62613  62624  2 

423  62634  62644  62655  62665  62675  62685  62696  62706  62716  62726 

424  62737  62747  62757  62767  62778  62788  62798  62808  62818  62829 

425  62839  62849  62859  62870  62880  62890  62900  62910  62921  62931 

426  62941  62951  62961  62972  62982  62992  63002  63012  63022  63033 

427  63043  63053  63063  63073  63083  63094  63104  63114  63124  63134 

428  63144  63155  63165  63175  63185  63195  63205  63215  63225  63236 

429  63246  63256  63266  63276  63286  63296  63306  63317  63327  63337 

430  63347  63357  63367  63377  63387  63397  63407  63417  63428  63438 

431  63448  63458  63468  63478  63488  63498  63508  63518  63528  63538 

432  63548  63558  63568  63579  63589  63599  63609  63619  63629  63639 

433  63649  63659  63669  63679  63689  63699  63709  63719  63729  63739 

434  63749  63759  63769  63779  63789  63799  63809  63819  63829  63839 

435  63849  63859  63869  63879  63889  63899  63909  63919  63929  63939 

436  63949  63959  63969  63979  63988  63998  64008  64018  64028  64038 

437  64048  64058  64068  64078  64088  64098  64108  64118  64128  64137 

438  64147  64157  64167  64177  64187  64197  64207  64217  64227  64237 

439  64246  64256  64266  64276  64286  64296  64306  64316  64326  64335 

440  64345  64355  64365  64375  64385  64395  64404  64414  64424  64434 

441  64444  64454  64464  64473  64483  64493  64503  64513  64523  64532 

442  64542  64552  64562  64572  64582  64591  64601  64611  64621  64631 

443  64640  64650  64660  64670  61680  64689  64699  64709  64719  64729 

444  64738  64748  64758  64768  64777  64787  64797  64807  64816  64826 

445  64836  64846  64856  64865  64875  64885  64895  64904  64914  64924 

446  64933  64943  64953  64963  64972  64982  64992  65002  65011  65021 

447  65031  65040  65050  65060  65070  65079  65089  65099  65108  65118 

448  65128  65137  65147  65157  65167  65176  65186  65196  65205  65215 

449  65225  65234  65244  65254  65263  65273  65283  65292  65302  65312 

450  65321  65331  65341  65350  65360  65369  65379  65389  65398  65408 


Tables.  Logarithms.  829 

10.        0          1          2845          6         7         8         9     Dif. 

450  65321  65831  65341  65350  65360  65369  65379  65389  65398  65408 

451  65418  65427  65437  65447  65456  65466  65475  65485  65495  65504 

452  65514  65523  65533  65543  65552  65562  65571  65581  65591  65600 

453  65610  65619  65629  65639  65648  65658  65667  65677  65686  65696 

454  65706  65715  65725  65734  65744  65753  65763  65772  65782  65792 

455  65801  65811  65820  65830  65839  65849  65858  65868  65877  65887 

456  65896  65906  65916  65925  65935  65944  65954  65963  65973  65982 

457  65992  66001  66011  66020  66030  66039  66049  66058  66068  66077 

458  66087  66096  66106  66115  66124  66134  66143  66153  66162  66172 

459  66181  66191  66200  66210  66219  66229  66238  66247  66257  66266 

460  66276  66285  66295  66304  66314  66323  66332  66342  66351  66361 

461  66370  66380  66389  66398  66408  66417  66427  66436  66445  66455 

462  66464  66474  66483  66492  66502  66511  66521  66530  66539  66549 

463  66558  66567  66577  66586  66596  66605  66614  66624  6G633  66642 

464  66652  66661  66671  66680  66689  66699  66708  66717  66727  66736 

465  66745  66755  66764  66773  66783  66792  66801  66811  66820  66829 

466  66839  66848  66857  66867  66876  66885  66894  66904  66913  66922 

467  66932  66941  66950  66960  66969  66978  66987  66997  67006  67015 

468  67025  67034  67043  67052  67062  67071  67080  67089  67099  67108 

469  67117  67127  67136  67145  67154  67164  67173  67182  67191  67201 

470  67210  67219  67228  67237  67247  67256  67265  67274  67284  67293  9 

471  67302  67311  67321  67330  67339  67348  67357  67367  67376  67385  '  ' 

472  67394  67403  67413  67422  67431  67440  67449  67459  67468  67477  2  2 

473  67486  67495  67504  67514  67523  67532  67541  67550  67560  67569 

474  67578  67587  67596  67605  67614  67624  67633  67642  67651  67660 

475  67669  67679  67688  67697  67706  67715  67724  67733  67742  67752 

476  67761  67770  67779  67788  67797  67806  67815  67825  97834  67843 

477  67852  67861  67870  67879  67888  67897  67906  67916  67925  67934 

478  67943  67952  67961  67970  67979  67988  67997  68006  68015  68024 

479  68034  68043  68052  68061  68070  68079  68088  68097  68106  68115 

480  68124  68133  68142  68151  68160  68169  68178  68187  68196  68205 

481  68215  68224  68233  68242  68251  68260  68269  68278  68287  68296 

482  68305  68314  68323  68332  68341  68350  68359  68368  68377  68386 

483  68395  68404  68413  68422  68431  68440  68449  68458  68467  68476 

484  68485  68494  68502  68511  68520  68529  68538  68547  68556  68565 

485  68574  68583  68592  68601  68610  68619  68628  68637  68646  68655 

486  68664  68673  68681  68690  68699  68708  68717  68726  68735  68744 

487  68753  68762  68771  68780  68789  68797  68806  68815  68824  68833 

488  68842  68851  68860  68869  68878  68886  68895  68904  68913  68922 

489  68931  68940  68949  68958  68966  68975  68984  68993  69002  69011 

490  69020  69028  69037  69046  69055  69064  69073  69082  69090  69099 

491  69108  69117  69126  69135  69144  69152  69161  69170  69179  69188 

492  69197  69205  69214  69223  69232  69241  69249  69258  69267  69276 

493  69285  69294  69302  69311  69320  69329  69338  69346  69355  69364 

494  69373  69381  69390  69399  69408  69417  69425  69434  69443  69452 

495  69461  69469  69478  69487  69496  69504  69513  69522  69531  69539 

496  69548  69557  69566  69574  69583  69592  69601  69609  69618  69627 

497  69636  69644  69653  69662  69671  69679  69688  69697  69705  69714 

498  69723  69732  69740  69749  69758  69767  69775  69784  69793  69801 

499  69810  69819  69827  69836  69845  69854  69862  69871  69880  69888 

500  69897  69906  69914  69923  69932  69940  69949  69958  69966  69975 


830  Logarithms.  Table  6. 

10.       0         I         *         3         4         5         6         7         8         9     u 

500  69897  69906  69914  69923  69932  69940  69949  69958  69966  69975  » 

501  69984  69992  70001  70010  70018  70027  70036  70044  70053  70062  1 

502  70070  70079  70088  70096  70105  70114  70122  70131  70140  70148  2 

503  70157  70165  70174  70183  70191  70200  70209  70217  70226  70234  3 

504  70243  70252  70260  70269  70278  70286  70295  70303  70312  70321  * 

505  70329  70338  70346  70355  70364  70372  70381  70389  70398  70406  8 

506  70415  70424  70432  70441  70449  70458  70467  70475  70484  70492  6 

507  70501  70509  70518  70526  70535  70544  70552  70561  70569  70578  7 

508  70586  70595  70603  70612  70621  70629  7063S  70646  70655  70063  • 

509  70672  70680  70689  70697  70706  70714  70723  70731  70740  70749  9 

510  70757  70766  70774  70783  70791  70800  70808  70817  70825  70834 

511  70842  70851  70859  70868  70876  70885  70893  70902  70910  70919 

512  70927  70935  70944  70952  70961  70969  70978  70986  70995  71003 

513  71012  71020  71029  71037  71046  71054  71063  71071  71079  71088 

514  71096  71105  71113  71122  71130  71139  71147  71155  71164  71172 

515  71181  71189  71198  71206  71214  71223  71231  71240  71248  71257 

516  71265  71273  71282  71290  71299  71307  71315  71324  71332  71341 

517  71349  71357  71366  71374  71383  71391  71399  71408  71416  71425 

518  71433  71441  71450  71458  71466  71475  71483  71492  71500  71508 

519  71517  71525  71533  71542  71550  71559  71567  71575  71584  71592 

520  71600  71609  71617  71625  71634  71642  71650  71659  71667  71675  i 

521  71684  71692  71700  71709  71717  71725  71734  71742  71750  71759  l 

522  71767  71775  71784  71792  71800  71809  71817  71825  71834  71842  2 

523  71850  71858  71867  71875  71883  71892  71900  71908  71917  71925  3 

524  71933  71941  71950  71958  71966  71975  71983  71991  71999  72008  4 

525  72016  72024  72032  72041  72049  72057  72066  72074  72082  72090  6 

526  72099  72107  72115  72123  72132  72140  72148  72156  72165  72173  6 

527  72181  72189  72198  72206  72214  72222  72230  72239  72247  72255  7 

528  72263  72272  72280  72288  72296  72304  72313  72321  72329  72337  8 

529  72346  72354  72362  72370  72378  72387  72395  72403  72411  72419  • 

530  72428  72436  72444  72452  72460  72469  72477  72485  72493  72501 

531  72509  72518  72526  72534  72542  72550  72558  72567  72575  72583 

532  72591  72599  72607  72616  72624  72632  72640  72648  72656  72665 

533  72673  72681  72689  72697  72705  72713  72722  72730  72738  72746 

534  72754  72762  72770  72779  72787  72795  72803  72811  72819  72827 

535  72835  72843  72852  72860  72868  72876  72884  72892  72900  72908 

536  72916  72925  72933  72941  72949  72957  72965  72973  72981  72989 

537  72997  73006  73014  73022  73030  73038  73046  73054  73062  73070 

538  73078  73086  73094  73102  73111  73119  73127  73135  73143  73151 

539  73159  73167  73175  73183  73191  73199  73207  73215  73223  73231 

540  73239  73247  73255  73263  73272  73280  73288  73296  73304  73312 

541  73320  73328  73336  73344  73352  73360  73368  73376  73384  73392 

542  73400  73408  73416  73424  73432  73440  73448  73456  73464  73472 

543  73480  73488  73496  73504  73512  73520  73528  73536  73544  73552 

544  73560  73568  73576  73584  73592  73600  73608  73616  73624  73632 

545  73640  73648  73656  73664  73672  73679  73687  73695  73703  73711 

546  73719  73727  73735  73743  73751  73759  73767  73775  73783  73791 

547  73799  73807  73815  73823  73830  73838  73846  73854  73862  73870 

548  73878  73886  73894  73902  73910  73918  73926  73933  73941  73949 

549  73957  73965  73973  73981  73989  73997  74005  74013  74020  74028 

550  74036  74044  74052  74060  74068  74076  74084  74092  74099  74107 


Table  6.  Logarithms.  831 

NO.       0         f         2        8         4        5         6         7         8        9      off 

550  74036  74044  74052  74060  74068  74076  74084  74092  74099  74107  » 

531  74115  74123  74131  74139  74147  74155  74162  74170  74178  74186  ll 

552  74194  74202  74210  74218  74225  74233  74241  74249  74257  74265  2a 

553  74273  74280  74288  74296  74304  74312  74320  74327  74335  74343  8» 

554  74351  74359  74367  74374  74382  74390  74398  74406  74414  74421  *8 

555  74429  74437  74445  74453  74461  74468  74476  74484  74492  74500  ** 

556  74507  74515  74523  74531  74539  74547  74554  74562  74570  74578  e* 

557  74586  74593  74601  74609  74617  74624  74632  74640  74648  74656  7  6 

558  74663  74671  74679  74687  74695  74702  74710  74718  74726  74733  8  ' 

559  74741  74749  74757  74764  74772  74780  74788  74796  74803  74811  9<7 

560  74819  74827  74834  74842  74850  74858  74865  74873  74881  74889 

561  74896  74904  74912  74920  74927  74935  74943  74950  74958  74966 

562  74974  74981  749S9  74997  75005  75012  75020  75028  75035  75043 

563  75051  75059  75066  75074  75082  75089  75097  75105  75113  75120 

564  75128  75136  75143  75151  75159  75166  75174  75182  75189  75197 

565  75205  75213  75220  75228  75236  75243  75251  75259  75266  75274 

566  75282  75289  75297  75305  75312  75320  75328  75335  75343  75351 

567  75358  75366  75374  75381  75389  75397  75404  75412  75420  75427 

568  75435  75442  75450  75458  75465  75473  75481  75488  75496  75504 

569  75511  75519  75526  75534  75542  75549  75557  75565  75572  75580 

570  75587  75595  75603  75610  75618  75626  75633  75641  75648  75656 

571  75664  75671  75679  75686  75694  75702  75709  75717  75724  75732 

572  75740  75747  75755  75762  75770  75778  75785  75793  75800  75808 

573  75815  75823  75831  75838  75846  75853  75861  75868  75876  75884 

574  75891  75899  75906  75914  75921  75929  75937  75944  75952  75959 

575  75967  75974  75982  75989  75997  76005  76012  76020  76027  76035 

576  76042  76050  76057  76065  76072  76080  76087  76095  76103  76110 

577  76118  76125  76133  76140  76148  76155  76163  76170  76178  76185 

578  76193  76200  76208  76215  76223  76230  76238  76245  76253  76260 

579  76268  76275  76283  76290  76298  76305  76313  76320  76328  76335 

580  76343  76350  76358  76365  76373  76380  76388  76395  76403  76410 

581  76418  76425  76433  76440  76448  76455  76462  76470  76477  76485 

582  76492  76500  76507  76515  76522  76530  76537  76545  76552  76559 

583  76567  76574  76582  76589  76597  76604  76612  76619  76626  76634 

584  76641  76649  76656  76664  76671  76678  76686  76693  76701  76708 

585  76716  76723  76730  76738  76745  76753  76760  76768  76775  76782 

586  76790  76797  76805  76812  76819  76827  76834  76842  76849  76856 

587  76864  76871  76879  76886  76893  76901  76908  76916  76923  76930 

588  76938  76945  76953  76960  76967  76975  76982  76989  76997  77004 

589  77012  77019  77026  77034  77041  77048  77056  77063  77070  77078 

590  77085  77093  77100  77107  77115  77122  77129  77137  77144  77151  * 

591  77159  77166  77173  77181  77188  77195  77203  77210  77217  77225  * 

592  77232  77240  77247  77254  77262  77269  77276  77283  77291  77298  2 

593  77305  77313  77320  77327  77335  77342  77349  77357  77364  77371  8 

594  77379  77386  77393  77401  77408  77415  77422  77430  77437  77444  4 

595  77452  77459  77466  77474  77481  77488  77495  77503  77510  77517  5 

596  77525  77532  77539  77546  77554  77561  77568  77576  77583  77590  e 

597  77597  77605  77612  77619  77627  77634  77641  77648  77656  77663  7 

598  77670  77677  77685  77692  77699  77706  77714  77721  77728  77735  8 

599  77743  77750  77757  77764  77772  77779  77786  77793  77801  77808  9 

600  77815  77822  77830  77837  77844  77851  77859  77866  77873  77880 


832  Logarithms.  Tables. 

10,      a         1         2         3         4         5         6         7         8         9       on 

600  77815  77822  77880  77837  77844  77851  77S59  77866  77873  77880 

601  77887  77895  77902  77909  77916  77924  77931  77938  77945  77952 

602  77960  77967  77974  77981  77988  77996  78003  78010  78017  78025 

603  78032  78039  78046  78053  78061  78068  78075  78082  78089  78097 

604  78104  78111  78118  78125  78132  78140  78147  78154  78161  78168 

605  78176  78183  78190  78197  78204  78211  78219  78226  78233  78240 

606  78247  78254  78262  78269  78276  78283  78290  78297  78305  78312 

607  78319  78326  78333  78340  78347  78355  78362  78369  78376  78383 

608  78390  78398  78405  78412  78419  78426  7843P,  78440  78447  78455 

609  78462  78469  78476  78483  78490  78497  78504  78512  78519  78526 

610  78533  78540  78547  78554  78561  78569  78576  78583  78590  78597 

611  78604  78611  78618  78625  78633  78640  78647  78654  78661  78608 

612  78675  78682  78689  78696  78704  78711  78718  78725  78732  78739 

613  78746  78753  78760  78767  78774  78781  78789  78796  78803  78810 

614  78817  78824  78831  78838  78845  78852  78859  78866  78873  78880 

615  78888  78895  78902  78909  78916  78923  78930  78937  78944  78951 

616  78958  78965  78972  78979  78986  78993  79000  79007  79014  79021 

617  79029  79036  79043  79050  79057  79064  79071  79078  79085  79092 

618  79099  79106  79113  79120  79127  79134  79141  79148  79155  79162 

619  79169  79176  79183  79190  79197  79204  79211  79218  79225  79232 

620  79239  79246  79253  7&260  79267  79274  79281  79288  79295  79302  ? 

621  79309  79316  79323  79330  79337  79344  79351  79358  79365  79372 '  ' 

622  79379  79386  79393  79400  79407  79414  79421  79428  79435  79442 2  » 

623  79449  79456  79463  79470  79477  79484  79491  79498  79505  79511 32 

624  79518  79525  79532  79539  79546  79553  79560  79567  79574  79581 43 

625  79588  79595  79602  79609  79616  79623  79630  79637  79644  79650 54 

626  79657  79964  79671  79678  79685  79692  79699  79706  79713  79720 64 

627  79727  79734  79741  79748  79754  79761  79768  79775  79782  79789 7S 

628  79796  79803  79810  79817  79824  79831  79837  79844  79851  79858 86 

629  79865  79872  79879  79886  79893  79900  79906  79913  79920  79927 9« 

630  79934  79941  79948  79955  79962  79969  79975  79982  79989  79996 

631  80003  80010  80017  80024  80030  80037  80044  80051  80058  80065 

632  80072  80079  80085  80092  80099  80106  80113  80120  80127  80134 

633  80140  80147  80154  80161  80168  80175  80182  80188  80195  80202 

634  80209  80216  80223  80229  80236  80243  80250  80257  80264  80271 

635  80277  80284  80291  80298  80305  80312  80318  80325  80332  80339 

636  80346  80353  80359  80366  80373  80380  80387  80393  80400  80407 

637  80414  80421  80428  80434  80441  80448  80455  80462  80468  80475 

638  80482  80489  80496  80502  80509  80516  80523  80530  80536  80543 

639  80550  80557  80561  80570  80577  80584  80591  80598  80604  80611 

640  80618  80625  80632  80638  80645  80652  80659  80665  80672  80679 

641  80686  80693  80699  80706  80713  80720  80726  80733  80740  80747 

642  80754  80760  80767  80774  80781  80787  80794  80801  80808  80814 

643  80821  80828  80835  80841  80848  80855  808o2  80868  80875  80882 

644  80889  80895  80902  80909  80916  80922  80929  80936  80943  80949 

645  80956  80963  80969  80976  80983  80990  80996  81003  81010  81017 

646  81023  81030  81037  81043  81050  81057  81064  81070  81077  81084 

647  81090  81097  81104  81111  81117  81124  81131  81137  81144  81151 

648  81158  81164  81171  81178  81184  81191  81198  81204  81211  81218 

649  81224  81231  81238  81245  81251  81258  81265  81271  81278  81285 

650  81291  81298  81305  81311  81318  81325  81331  81338  81345  81351 


rabies.  Logarithms.  .  833 

FO.   0    f    2    S    4    5    6    7    8    9   oif. 

650  8129J  8129$  81305  81311  81318  81325  81331  81338  81345  81351  ? 

651  81358  81365  81371  81378  81385  81391  81398  81405  81411  81418  >  ! 

652  81425  81431  81438  81445  81451  81458  81465  81471  81478  81485  ~  ' 

653  81491  81498  81505  81511  81518  81525  81531  81538  81544  81551  s- 

654  81558  81564  81571  81578  81584  81591  81598  81604  81611  81617  48 

655  81624  81631  81637  81644  81651  81657  81664  81671  81677  81684  »4 

656  81690  81697  81704  81710  81717  81723  81730  81737  81743  81750  64 

657  81757  81763  81770  81776  81783  81790  81796  81803  81809  81816  7£ 

658  81823  81829  81836  81842  81849  81856  81862  81869  81875  81882  8  6 

659  81889  81895  81902  81908  81915  81921  81928  81935  81941  81948  9  e 

660  81954  81961  81968  81974  81981  81987  81994  82000  82007  82014 

661  82020  82027  82033  82040  82046  82053  82060  82066  82073  82079 

662  82086  82092  82099  82105  82112  82119  82125  82132  82138  82145 

663  82151  82158  82164  82171  82178  82184  82191  82197  82204  82210 

664  82217  82223  82230  82236  82243  82249  82256  82263  82269  82276 

665  82282  82289  82295  82302  82308  82315  82321  82328  82334  82341 

666  82347  82354  82360  82367  82373  82380  82387  82393  82400  82406 

667  82413  82419  82426  82432  82439  82445  82452  82458  82465  82471 

668  82478  82484  82491  82497  82504  82510  82517  82523  82530  82536 

669  82543  82549  82556  82562  82569  82575  82582  82588  82595  82601 

670  82607  82614  82620  82627  82633  82640  82646  82653  82659  82666 

671  82672  82679  82685  82692  82698  82705  82711  82718  82724  82730 

672  82737  82743  82750  82756  82763  82769  82776  82782  82789  82795 

673  82S02  82808  82814  82821  82827  82834  82840  82847  82853  82800 

674  82866  82872  82879  82885  82892  82898  82905  82911  82918  82924 

675  82930  82937  82943  82950  82956  82963  82969  82975  82982  82988 

676  82995  83001  8300S  83014  83020  83027  83033  83040  83046  83052 

677  83059  83065  83072  83078  83085  83091  83097  83104  83110  83117 

678  83123  83129  83136  83142  83149  83155  83161  83168  83174  83181 

679  83187  83193  83200  83206  83213  83219  83225  83232  83238  83245 

680  83251  83257  83264  83270  83276  83283  83289  83296  83302  83308 

681  83315  83321  83327  83334  83340  83347  83353  83359  83366  83372 

682  S3378  833S5  83391  83398  83404  83410  83417  83423  83429  83436 

683  83442  83448  83455  83461  83467  83474  83480  83487  83493  83499 

684  83506  83512  83518  83525  83531  83537  83544  83550  83556  83563 

685  83569  83575  83582  83588  83594  83601  83607  83613  83620  83626 

686  83632  83639  83C45  83C51  83658  83664  83670  83677  83683  83689 

687  83690  83702  S3708  83715  83721  83727  83734  83740  83746  83753 

688  83759  83765  83771  83778  83784  83790  83797  83803  83809  83816 

689  SH822  83828  83835  83841  83847  83853  83860  83866  83872  83879  9  * 

690  83885  83891  83897  83904  83910  83916  83923  83929  83935  83942 
091  83948  83954  83960  83967  83973  83979  83985  83992  83998  84004 

692  S4011  84017  84023  84029  84036  84042  84048  84055  84061  84067 

693  84073  84080  84086  84092  84098  84105  84111  84117  84123  84130 

694  84136  84142  84148  84155  84161  84167  84173  84180  84186  84192 

695  84198  84205  84211  84217  84223  84230  84236  84242  84248  84255 

696  84261  84267  S4273  84280  84286  84292  84298  84305  84311  84317 

697  84323  84330  84336  84342  84348  84354  84361  84367  84373  84379 

698  84386  S4392  84398  84404  84410  84417  84423  84429  84435  84442 

699  84148  84454  84460  S44G6  8-1473  84479  84485  84491  84497  84504 

700  84510  84516  84522  84528  S4535  84541  84547  84553  84559  84566 


834  Logarithms.  Table6 

50.      fllt345«789     on. 

700  84510  84516  84522  84528  84535  84541  84547  84553  84559  84566 

701  84572  84578  84584  84590  84597  84603  84609  84615  84621  84628 

702  84634  84640  84646  84652  84658  84665  84671  84677  84083  84689 

703  84696  84702  84708  84714  84720  84726  84733  84739  84745  84751 

704  84757  84763  84770  84776  84782  84788  84794  84800  84807  84813 

705  84819  84825  84831  84837  84844  84850  84856  84862  84868  84874 

706  84880  84887  84893  84899  84905  84911  84917  84924  84930  84936 

707  84942  84948  84954  84960  84967  84973  84979  84985  84991  84997 

708  85003  85009  85016  85022  85028  85034  85040  85046  85052  85058 

709  85065  85071  85077  85083  85089  85095  85101  85107  85114  85120 

710  85126  85132  85138  85144  85150  85156  85163  85169  85175  85181 

711  85187  85193  85199  85205  85211  85217  85224  85230  85236  85242 

712  85248  85254  85260  85266  85272  85278  85285  85291  85297  85303 

713  85309  85315  85321  85327  85333  85339  85345  85352  85358  85364 

714  85370  85376  85382  85388  85394  85400  85406  85412  85418  85425 

715  85431  85437  85443  85449  85455  85461  85467  85473  85479  85485 

717  85491  85497  85503  85509  85516  85522  85528  85534  85540  85546 

716  85552  85558  85564  85570  85576  85582  85588  85594  85600  85606 

718  85612  85618  85625  85631  85637  85643  85649  85655  85661  85667 

719  85673  85679  85685  85691  85697  85703  85709  85715  85721  85727 

720  85733  85739  85745  85751  85757  85763  85769  85775  85781  85788  e 

721  85794  85800  85806  85812  85818  85824  85830  85836  85842  85848  l  1 

722  85854  85860  85866  85872  85878  85884  85890  85896  85902  85908  2  1 

723  85914  85920  85926  85932  85938  85944  85950  85956  85962  85968 

724  85974  85980  85986  85992  85998  86004  86010  86016  86022  86028 

725  86034  86040  86046  86052  86058  86064  86070  86076  86082  86088 

726  86094  86100  86106  86112  86118  86124  86130  86136  86141  86147 

727  86153  86159  86165  86171  86177  86183  86189  86195  86201  86207 

728  86213  86219  86225  86231  86237  86243  86249  86255  86261  86267 

729  86273  86279  86285  86291  86297  86303  86308  86314  86320  86326 

730  86332  86338  86344  86350  86356  86362  86368  86374  86380  86386 
7H1  86392  86398  86404  86410  86415  86421  86427  86433  86439  86446 

732  86451  86457  86463  86469  86475  86481  86487  86493  86499  86504 

733  86510  86516  86522  86528  86534  86540  86546  86552  86558  86564 

734  86570  86576  86581  86587  86593  86599  86605  86611  86617  86623 

735  86629  86635  86641  86646  86652  86658  86664  86670  86676  86682 

736  86688  86694  86700  86705  86711  86717  86723  86729  86735  86741 

737  86747  86753  86759  86764  86770  86776  86782  86788  86794  86800 

738  86806  86812  86817  86823  86829  86835  86841  86847  86853  86859 

739  86864  86870  86876  86882  86888  86894  86900  86906  86911  86917 

740  86923  86929  86935  86941  86947  86953  86958  86964  86970  86976 

741  86982  86988  86994  86999  87005  87011  87017  87023  87029  87035 

742  87040  87046  87052  87058  87064  87070  87075  87081  87087  87093 

743  87099  87105  87111  87116  87122  87128  87134  87140  87146  87151 

744  87157  87163  87169  87175  87181  87186  87192  87198  87204  87210 

745  87216  87221  87227  87233  87239  87245  87251  87256  87262  87268 

746  87274  87280  87286  87291  87297  87303  87309  87315  87320  87326 

747  87332  87338  87344  87349  87355  87361  87367  87373  87379  87384 

748  87390  87396  87402  87408  87413  87419  87425  87431  87437  87442 

749  87448  87454  87460  87466  87471  87477  87483  87489  87495  87500 

750  87506  87512  87518  87523  87529  87535  87541  87547  87552  87558 


Table  6.  Logarithms.  835 

10.       0123456780      oif. 

750  87506  87512  87518  87523  87529  87535  87541  87547  87552  87558 

751  87564  87570  87576  87581  87587  87593  87599  87604  87610  87616 

752  87622  87628  87633  87639  87645  87651  87656  87662  87668  87674 

753  87679  87685  87691  87697  87703  87708  87714  87720  87726  87731 

754  87737  87743  87749  87754  87760  87766  87772  87777  87783  87789 

755  87795  87800  87806  87812  87818  87823  87829  87835  87841  87846 

756  87852  87858  87864  87869  87875  87881  87887  87892  87898  87904 

757  87910  87915  87921  87927  87933  87938  87944  87950  87955  87961 

758  87967  87973  87978  87984  87990  87996  88001  88007  88013  88018 
750  88024  88030  88036  88041  88047  88053  88058  88064  88070  88076 

760  88081  88087  88093  88098  88104  88110  88116  88121  88127  88133 

761  88138  88144  88150  88156  88161  88167  88173  88178  88184  88190 

762  88195  88201  88207  88213  88218  88224  88230  88235  88241  88247 

763  88252  88258  88264  88270  88275  88281  88287  88292  88298  88304 

764  88309  88315  88321  88326  88332  88338  88343  88349  88355  88360 

765  88366  88372  88377  88383  88389  88395  88400  88406  88412  88417 

766  88423  88429  88434  88440  88446  88451  88457  88463  88468  88474 

767  88480  88485  88491  88497  88502  88508  88513  88519  88525  88530 

768  88536  88542  88547  88553  88559  88564  88570  88576  88581  88587 
760  88593  88598  88604  88610  88615  88621  88627  88632  88638  88643 

770  88649  88655  88660  88666  88672  88677  88683  88689  88694  88700    e 

771  88705  88711  88717  88722  88728  88734  88739  88745  88750  88756  l  » 

772  88762  88767  88773  88779  88784  88790  88795  88801  88807  88812  * » 

773  88818  88824  88829  88835  88840  88846  88852  88857  88863  88868  3  * 

774  88874  88880  88885  88891  88897  88902  88908  88913  88919  88925  4  2 

775  88930  88936  88941  88947  88953  88958  88964  88969  88975  88981  5  8 

776  88986  88992  38997  89003  89009  89014  89020  89025  89031  89037  e  4 

777  89042  89048  89053  89059  89064  89070  89076  89081  89087  89092  7  4 

778  89098  8910  i  89109  89115  89120  89126  89131  89137  89143  89148  8« 
770  89154  89159  89165  89170  89176  89182  89187  89193  89198  89204  9 fi 

780  89209  89215  89221  89226  89232  89237  89243  89248  89254  89260 

781  89265  89271  89276  89282  89287  89293  89298  89304  89310  89315 

782  89321  89326  89332  89337  89343  89348  89354  89360  89365  89371 

783  89376  89382  89387  89393  89398  89404  89409  89415  89421  89426 

784  89432  89437  89443  89448  89454  89459  89465  89470  89476  89481 

785  89487  89492  89498  89504  89509  89515  89520  89526  89531  89537 

786  89542  89548  89553  89559  89564  89570  89575  89581  89586  89592 

787  89597  89603  89609  89614  89620  89625  89631  89636  89642  89647 

788  89653  89658  89664  89669  89675  89680  89686  89691  89697  89702 
780  89708  89713  89719  89724  89730  89735  89741  89746  89752  89757 

700  89763  89768  89774  89779  89785  89790  89796  89801  89807  89812 

701  89818  89823  89829  89834  89840  89845  89851  89856  89862  89867 

702  89873  89878  89883  89889  89894  89900  89905  89911  89916  89922 

703  89927  89933  89938  89944  89949  89955  89960  89966  89971  89977 

704  89982  89988  89993  89998  90004  90009  90015  90020  90026  90031 

705  90037  90042  90048  90053  90059  90064  90069  90075  90080  90086 

706  90091  90097  90102  90108  90113  90119  90124  90129  90135  90140 

797  90146  00151  90157  90162  90168  90173  90179  90184  90189  90195 

798  90200  90206  90211  90217  90222  90227  90233  90238  90244  90249 

799  90255  90260  90266  90271  90276  90282  90287  90293  90298  90304 

800  90309  90314  90320  90325  90331  90336  90342  90347  90352  90358 


836  Logarithms.  Table  6. 

10,       OI28456739W. 

800  90309  90314  90320  90325  90331  90336  90342  90347  90352  90358 

801  90363  90369  90374  90380  90385  90390  90396  90401  90407  90412 

802  90417  90423  90428  90434  90439  90445  90450  90455  90461  90466 

803  90472  90477  90482  90488  90493  90499  90504  90509  90515  90520 

804  90526  90531  90536  90542  90547  90553  90558  90563  90569  90574 

805  90580  90585  90590  90596  90601  90607  90612  90617  90623  90628 

806  90634  90639  90644  90650  90655  90660  90666  90671  90677  90682 

807  90687  90693  90698  90703  90709  90714  90720  90725  90730  90736 

808  90741  90747  90752  90757  90763  90768  90773  90779  90784  90789 

809  90795  90800  90806  90811  90816  90822  90827  90832  90838  90843 

810  90849  90854  90859  90865  90870  90875  90881  90886  90891  90897 

811  90902  90907  90913  90918  90924  90929  90934  90940  90945  90950 

812  90956  90961  90966  90972  90977  90982  90988  90993  90998  91004 

813  91009  91014  91020  91025  91030  91036  91041  91046  91052  91057 

814  91062  91068  91073  91078  91084  91089  91094  91100  91105  91110 

815  91116  91121  91126  91132  91137  91142  91148  91153  91158  91164 

816  91169  91174  91180  91185  91190  91196  91201  91206  91212  91217 

817  91222  91228  91233  91238  91243  91249  91254  91259  91265  91270 

818  91275  91281  91286  91291  91297  91302  91307  91312  91318  91323 

819  91328  91334  91339  91344  91350  91355  91360  91365  91371  91376 

820  91381  91387  91392  91397  91403  91408  91413  91418  91424  91429  & 

821  91434  91440  91445  91450  91455  91461  91466  91471  91477  91482  *  > 

822  91487  91492  91498  91503  91508  91514  91519  91524  91529  91535 2  » 

823  91540  91545  91551  91556  91561  91566  91572  91577  91582  91587 8* 

824  91593  91598  91603  91609  91614  91619  91624  91630  91635  91640 4  2 

825  91645  91651  91656  91661  91666  91672  91677  91682  91687  91693 6$ 

826  91698  91703  91709  91714  91719  91724  91730  91735  91740  91745 6  8 

827  91751  91756  91761  91766  91772  91777  91782  91787  91793  91798 7* 

828  91803  91808  91814  91819  91824  91829  91834  91840  91845  91850 84 

829  91855  91861  91866  91871  91876  91882  91887  91892  91897  91903 9I 

830  91908  91913  91918  91924  91929  91934  91939  91944  91950  91955 

831  91960  91965  91971  91976  91981  91986  91991  91997  92002  92007 

832  92012  92018  92023  92028  92033  92038  92044  92049  92054  92059 

833  92065  92070  92075  92080  92085  92091  92096  92101  92106  92111 

834  92117  92122  92127  92132  92137  92143  92148  92153  92158  92163 

835  92169  92174  92179  92184  92189  92195  92200  92205  92210  92215 

836  92221  92226  92231  92236  92241  92247  92252  92257  92262  92267 

837  92273  92278  92283  92288  92293  92298  92304  92309  92314  92319 

838  92324  92330  92335  92340  92345  92350  92355  92361  92366  92371 

839  92376  92381  92387  92392  92397  92402  92407  92412  92418  92425 

840  92428  92433  92438  92443  92449  92454  92459  92464  92469  92474 

841  92480  92485  92490  92495  92500  92505  92511  92516  92521  92526 

842  92531  92536  92542  92547  92552  92557  92562  92567  92572  92578 

843  92583  92588  92593  92598  92603  92609  92614  92619  92624  92629 

844  92634  92639  92645  92650  92655  92660  92665  92670  92675  92681 

845  92686  92691  92696  92701  92706  92711  92716  92722  92727  92732 

846  92737  92742  92747  92752  92758  92763  92768  92773  92778  92783 

847  92788  92793  92799  92804  92809  92814  92819  92824  92829  92834 

848  92840  92845  92850  92855  92860  92865  92870  92875  92881  92886 

849  92891  92896  92901  92906  92911  92916  92921  92927  92932  92937 

850  92942  92947  92952  92957  92962  92967  92973  92978  929S3  92988 


Table  6.  Logarithms.  837 

HO.       01         2345          6739    on 

850  92942  92947  92952  92957  92962  92967  92973  92978  92983  92988 

851  92993  92998  93003  93008  93013  93018  93024  93029  93034  93039 

852  93044  93049  93054  93059  93064  93069  93075  93080  93085  93090 

853  93095  93100  93105  93110  93115  93120  93125  93131  93136  93141 

854  93146  93151  93156  93161  93166  93171  93176  93181  93186  93192 

855  93197  93202  93207  93212  93217  93222  93227  93232  93237  93242 
850  93247  93252  93258  93263  93268  93273  93278  93283  93288  93293 

857  93298  93303  93308  93313  93318  93323  93328  93334  93339  93344 

858  93349  93354  93359  93364  93369  93374  93379  93384  93389  93394 

859  93399  93404  93409  93414  93420  93425  93430  93435  93440  93445 

860  93450  93455  93460  93465  93470  93475  93480  93485  93490  93495 

861  93500  93505  93510  93515  93520  93526  93531  93536  93541  93546 

862  93551  93556  93561  93566  93571  93576  93581  93586  93591  93596 

863  93601  93606  93611  93616  93621  93626  93631  93636  93641  93646 

864  93651  93656  93661  93666  93671  93676  93682  93687  93692  93697 

865  93702  93707  93712  93717  93722  93727  93732  93737  93742  93747 

866  93752  93757  93762  93767  93772  93777  93782  93787  93792  93797 

867  93802  93807  93812  93817  93822  93827  93832  93837  93842  93847 

868  93852  93857  93862  93867  93872  93877  93882  93887  93892  93897 

869  93902  93907  93912  93917  93922  93927  93932  93937  93942  93947 

870  93952  93957  93962  93967  93972  93977  93982  93987  93992  93997  * 

871  94002  94007  94012  94017  94022  94027  94032  94037  94042  94047  l 

872  94052  94057  94062  94067  94072  94077  94082  94086  94091  94096  2 

873  94101  94106  94111  94116  94121  94126  94131  94136  94141  9414C 3 

874  94151  94156  94161  94166  94171  94176  94181  94186  94191  94190* 

875  94201  94206  94211  94216  94221  94226  94231  94236  94240  94245s 

876  94250  94255  94260  94265  94270  94275  94280  94285  94290  94295  6 

877  94300  94305  94310  94315  94320  94325  94330  94335  94340  94345 7* 

878  94349  94354  94359  94364  94369  94374  94379  94384  94389  94394s* 

879  94399  94404  94409  94414  94419  94424  94429  94433  94438  94443 9f 

880  94448  94453  94458  94463  94468  94473  94478  94483  94488  94493 

881  94498  94503  94507  94512  94517  94522  94527  94532  94537  94542 

882  94547  94552  94557  94562  94567  94571  94576  94581  94586  94591 

883  94596  94601  94606  94611  94616  94621  94626  94630  94635  94640 

884  94645  94650  94655  94660  94665  94670  94675  94680  94685  94689 

885  94694  94699  94704  94709  94714  94719  94724  94729  94734  94738 

886  94743  94748  94753  94758  94763  94768  94773  94778  94783  94787 

887  94792  94797  94802  94807  94812  94817  94822  94827  94832  94836 

888  94841  94846  94851  94856  94861  94866  94871  94876  94880  94885 

889  94890  94895  94900  94905  94910  94915  94919  94924  94929  94934 

890  94939  94944  94949  94954  94959  94963  94968  94973  94978  94988 

891  94988  94993  94998  95002  95007  95012  95017  95022  95027  95032 

892  95036  95041  -95046  95051  95056  95061  95066  95071  95075  95080 

893  95085  95090  95095  95100  95105  95109  95114  95119  95124  95129 

894  95134  95139  95143  95148  95153  95158  95163  95168  95173  95177 

895  95182  95187  95192  95197  95202  95207  95211  95216  95221  95226 

896  95231  95236  95240  95245  95250  95255  95260  95265  95270  95274 

897  95279  95284  95289  95294  95299' 95303  95308  95313  95318  95323 

898  95328  95332  95337  95342  95347  95352  95357  95361  95366  95371 

899  95376  95381  95386  95390  95395  95400  95405  95410  95415  95419 

900  95424  95429  95434  95439  95444  95448  95453  95458  95463  9546S 


838  Logarithms.  Table  6. 

10,   0    1    2    3    4    5    6    7    8    9  OK, 

900  95424  95429  95434  95439  95444  95448  95453  95158  95463  95468 

901  95472  95477  95482  95487  95492  95497  95501  95506  95511  95516 

902  95521  95525  95530  95535  95540  95545  95550  95554  95559  95564 

903  95569  95574  95578  95583  95588  95593  95598  95602  95607  95612 

904  95617  95622  95626  95631  95636  95641  95646  95650  95655  95660 

905  95665  95670  95674  95679  95684  95689  95694  95698  95703  95708 

906  95713  95718  95722  95727  95732  95737  95742  95746  95751  95756 

907  95761  95766  95770  95775  95780  95785  95789  95794  95799  95804 

908  95809  95813  95818  95823  95828  95832  95837  95842  95847  95852 

909  95856  95861  95866  95871  95875  95880  95885  95890  95895  95899 

910  95904  95909  95914  95918  95923  95928  95933  95938  95942  9594V 

911  95952  95957  95961  95966  95971  95976  95980  95985  95990  95995 

912  95999  96004  96009  96014  96019  96023  96028  96033  96038  96042 

913  96047  96052  96057  96061  96066  96071  96076  96080  96085  96090 

914  96095  96099  96104  96109  96114  96118  96123  96128  96133  96137 

915  96142  96147  96152  96156  96161  96166  96171  96175  96180  96185 

916  96190  96194  96199  96204  96209  96213  96218  96223  96227  96232 

917  96237  96242  96246  96251  96256  96261  96265  96270  96275  96280 

918  96284  96289  96294  96298  96303  96308  96313  96317  96322  96327 

919  96332  96336  96341  96346  96350  96355  96360  96365  96369  96374 

920  96379  96384  96388  96393  96398  96402  96407  96412  96417  96421  & 

921  96426  96431  96435  96440  96445  96450  96454  96459  96464  96468  J  > 

922  96473  96478  96483  96487  96492  96497  96501  96506  96511  96515  2  l 

923  96520  96525  96530  96534  96539  96544  96548  96553  96558  96562  3  2 

924  96567  96572  96577  96581  96586  96591  96595  96600  96605  96609  4  2 

925  96614  96619  96624  96628  96633  96638  96642  96647  96652  96656  * 

926  96661  96666  96670  96675  96680  96685  96689  96694  96699  96703  e 

927  96708  96713  96717  96722  96727  96731  96736  96741  96745  96750  7 

928  96755  96759  96764  96769  96774  96778  96783  96788  96792  96797  8 

929  96802  96806  96811  96816  96820  96825  96830  96834  96839  96844  • 

930  96848  96853  96858  96862  96867  96872  96876  96881  96886  96890 

931  96895  96900  96904  96909  96914  96918  96923  96928  96932  96937 

932  96942  96946  96951  96956  96960  96965  96970  96974  96979  96984 

933  96988  96993  96997  97002  97007  97011  97016  97021  97025  97030 

934  97035  97039  97044  97049  97053  97058  97063  97067  97072  97077 

935  97081  97086  97090  97095  97100  97104  97109  97114  97118  97123 

936  97128  97132  97137  97142  97146  97151  97155  97160  97165  97169 

937  97174  97179  97183  97188  97192  97197  97202  97206  97211  97216 

938  97220  97225  97230  97234  97239  97243  97248  97253  97257  97262 

939  97267  97271  97276  97280  97285  97290  97294  97299  97304  97308 

940  97313  97317  97322  97327  97331  97336  97340  97345  97350  97354 

941  97359  97364  97368  97373  97377  97382  97387  97391  97396  97400 

942  97405  97410  97414  97419  97424  97428  97433  97437  97442  97447 

943  97451  97456  97460  97465  97470  97474  97479  97483  97488  97493 

944  97497  97502  97506  97511  97516  97520  97525  97529  97534  97539 

945  97543  97548  97552  97557  97562  97566  97571  97575  97580  97585 

946  97589  97594  97598  97603  97607  97612  97617  97621  97626  97630 

947  97635  97640  97644  97649  97653  97658  97663  97667  97672  97676 

948  97681  97685  97690  97695  97699  97704  97708  97713  97717  97722 

949  97727  97731  97736  97740  97745  97749  97754  97759  97763  97768 

950  97772  97777  97782  97786  97791  97795  97800  97804  97809  97813 


Table  6.  Logarithms.  839 

Ko,      0         1         *         8         4         5         6         7         8         0     OH. 

950  97772  97777  97782  97786  97791  97795  97800  97804  97809  97813  * 

951  97818  97823  97827  97832  97836  97841  97845  97850  97855  97859  1 1 

952  97864  97868  97873  97877  97882  97886  97891  97896  97900  97905  a  l 

953  97909  97914  97918  97923  97928  97932  97937  97941  97946  97950  8  * 

954  97955  97959  97964  97968  97973  97978  97982  97987  97991  97996  * 2 

955  98000  98005  98009  98014  98019  98023  98028  98032  98037  98041  8  * 

956  98046  98050  98055  98059  98064  98068  98073  98078  98082  98087  6  * 

957  98091  98096  98100  98105  98109  98114  98118  98123  98127  98132  T* 

958  98137  98141  98146  98150  98155  98159  98164  98168  98173  98177  8« 

959  98182  98186  98191  98195  98200  98204  98209  98214  98218  98223  9* 

960  98227  98232  98236  98241  98245  98250  98854  98259  98263  98268 

961  98272  98277  98281  98286  98290  98295  98299  98304  98308  98313 

962  98318  98322  98327  98331  98336  98340  98345  98349  98354  98358 

963  98363  98367  98372  98376  98381  98385  98390  98394  98399  98408 

964  98408  98412  98417  98421  98426  98430  98435  98439  98444  98448 

965  98453  98457  98462  98466  98471  98475  98480  98484  98489  98493 

966  98498  98502  98507  98511  98516  98520  98525  98529  98534  98588 

967  98543  98547  98552  98556  98561  98565  98570  98574  98579  98583 

968  98588  98592  98597  98601  98605  98610  98614  98619  98623  98628 

969  98632  98637  98641  98646  98650  98655  98659  98664  98668  98673 

970  98677  98682  98686  98691  98695  98700  98704  98709  98713  98717 

971  98722  98726  98731  98735  98740  98744  98749  98753  98758  98762 

972  98767  98771  98776  98780  98784  98789  98793  98798  98802  98807 

973  98811  98816  98820  98825  98829  98834  98838  98843  98847  98851 

974  98856  98860  98865  98869  98874  98878  98883  98887  98892  98896 

975  98900  98905  98909  98914  98918  98923  98927  98932  98936  98941 

976  98945  98949  98954  98958  98963  98967  98972  98976  98981  98985 

977  98989  98994  98998  99003  99007  99012  99016  99021  99025  990&0 

978  99034  99038  99043  99047  99052  99056  99061  99065  99069  99074 

979  99078  99083  99087  99092  99096  99100  99105  99109  99114  99118 

980  99123  99127  99131  99136  99140  99145  99149  99154  99158  99162 

981  99167  99171  99176  99180  99185  99189  99193  99198  99202  99207 

982  99211  99216  99220  99224  99229  99233  99238  99242  99247  99251 

983  99255  99260  99264  99269  99273  99277  99282  99286  99291  99295 

984  99300  99304  99308  99313  99317  99322  99326  99330  99335.99339 

985  99344  99348  99352  99357  99361  99366  99370  99374  99379  99383 

986  99388  99392  99396  99401  99405  99410  99414  99419  99423  99427 

987  99432  99436  99441  99445  99449  99454  99458  99463  99467  99471 

988  99476  99480  99484  99489  99493  99498  99502  99506  99511  99515 

989  99520  99524  99528  99533  99537  99542  99546  99550  99555  99559 

990  99564  99568  99572  99577  99581  99585  99590  99594  99599  99603  * 

991  99607  99612  99616  99621  99625  99629  99634  99638  99642  99647  lf 

992  99651  99656  9&660  99664  99669  99673  99677  99682  99686  99691 

993  99695  99699  99704  99708  99712  99717  99721  99726  99730  99734 

994  99739  99743  99747  99752  99756  99760  99765  99769  99774  99778 

995  99782  99787  99791  99795  99800  99804  99808  99813  99817  99822 

996  99826  99830  99835  99839  99843  99848  99852  99856  99861  99865 

997  99870  99874  99878  998$3  99887  99891  99896  99900  99904  99909 

998  99913  99917  99922  99926  99930  99935  99939  99944  99948  99952 

999  99957  99961  99965  99970  99974  99978  99983  99987  99991  99996 

1000  00000  00004  00009  00013  00017  00022  00026  00030  00035  00039 


840  Logarithms.  Table  6. 

0133456780    OK 

1000  00000  00004  00009  00013  00017  00022  00026  00030  00035  00039 

1001  00043  00048  00052  00056  00061  00065  00069  00074  00078  00082 

1002  00087  00091  00095  00100  00104  00108  00113  00117  00121  00126 

1003  00130  00134  00139  00143  00147  00152  00156  00160  00165  00169 

1004  00173  00178  00182  00186  00191  00195  00199  00204  00208  00212 

1005  00217  00221  00225  00230  00234  00238  00243  00247  00251  00255 

1006  00260  00264  00268  00273  00277  00281  00286  00290  00294  00299 

1007  00303  00307  00312  00316  00320  00325  00329  00333  00337  00342 

1008  00346  00350  00355  00359  00363  00368  00372  00376  00381  00385 

1009  00389  00393  00398  00402  00406  00411  00415  00419  00424  00428 

1010  00432  00436  00441  00445  00449  00454  00458  00462  00467  00^71 

1011  00475  00479  00484  00488  00492  00497  00501  00505  00509  00514 

1012  00518  00522  00527  00531  00535  00540  00544  00548  00552  00557 

1013  00561  00565  00570  00574  00578  00582  00587  00591  00595  00600 

1014  00604  00608  00612  00617  00621  00625  00629  00634  00638  00642 

1015  00647  00651  00655  00659  00664  00668  00672  00677  00681  OOG85 

1016  00689  00694  00698  00702  00706  00711  00715-00719  00724  00728 

1017  00732  00736  00741  00745  00749  00753  00758  00762  00766  00771 

1018  00775  00779  00783  00788  00792  00796  00800  00805  00809  00813 

1019  00817  00822  00826  00830  00834  00839  00843  00847  00852  00856 

1020  00860  00864  00869  00873  00877  00881  00886  00890  00894  00898  * 

1021  00903  00907  00911  00915  00920  00924  00928  00932  00937  00941 l  ° 

1022  00945  00949  00954  00958  00962  00966  00971  00975  00979  00983 2  » 

1023  00988  00992  00996  01000  01005  01009  01013  01017  01022  01026 8  ' 

1024  01030  01034  01038  01043  01047  01051  01055  01060  01064  01068* 2 

1025  01072  01077  01081  01085  01089  01094  01098  01102  01106  01111 52 

1026  01115  01119  01123  01127  01132  01136  01140  01144  01149  01153 62 

1027  01157  01161  01166  0117001174  01178  01182  01187  01191  01195 73 

1028  01199  01204  01208  01212  01216  01220  01225  01229  01233  01237 8  3 

1029  01242  01246  01250  01254  01258  01263  01267  01271  01275  01280 9  4 

1030  01284  01288  01292  01296  01301  01305  01309  01313  01317  01322 

1031  01326  01330  01334  01339  01343  01347  01351  01355  01360  013G4 

1032  01368  01372  01376  01381  01385  01389  01393  01397  01402  01406 

1033  01410  01414  01418  01423  01427  01431  01435  01439  01444  01448 

1034  01452  01456  01460  01465  01469  01473  01477  01481  01486  014CO 

1035  01494  01498  01502  01507  01511  01515  01519  01523  01528  01532 

1036  01536  01540  01544  01549  01553  01557  01561  01565  01569  01574 

1037  01578  01582  01586  01590  01595  01599  01603  01607  01611  01616 

1038  01620  01624  01628  01632  01636  01641  01645  01649  01653  01657 

1039  01662  01666  01670  01674  01678  01682  01687  01691  01695  01699 

1040  01703  01708  01712  01716  01720  01724  01728  01733  01737  01741 

1041  01745  01749  01753  01758  01762  01766  01770  01774  01778  01783 

1042  01787  01791  01795  01799  01803  01808  01812  01816  01820  01824 

1043  01828  01833  01837  01841  01845  01849  01853  01858  01862  01866 

1044  01870  01874  01878  01883  01887  01891  01895  01899  01903  01907 

1045  01912  01916  01920  01924  01928  01932  01937  01941  01945  01949 

1046  01953  01957  01961  01966  01970  01974  01978  01982  01986  01991 

1047  01995  01999  02003  02007  02011  02015  02020  02024  02028  02032 

1048  02036  02040  02044  02049  02053  02057  02061  02065  02069  02073 

1049  02078  02082  02086  02090  02094  02098  02102  02107  02111  02115 

1050  02119  02123  02127  02131  02135  02140  02144  02148  02152  02156 


6.  Logarithms.  841 

G         f         *        3         4        5         6        7         8        9     M. 

1050  02119  02123  02127  02181  02135  02140  02144  02148  02152  02156 

1051  02100  02164  02169  02173  02177  02181  02185  02189  02193  02197 

1052  02202  02206  02210  02214  02218  02222  02226  02230  02235  02239 

1053  02243  02247  02251  02255  02259  02263  02268  02272  02276  02280 

1054  02284  02288  02292  02296  02301  02305  02309  02313  02317  02321 

1055  02325  02329  02333  02338  02342  02346  02350  02354  02358  02362 

1056  02366  02371  02375  02379  02383  02387  02391  02395  02399  02403 

1057  02407  02412  02416  02420  02424  02428  02432  02436  02440  02444 

1058  02449  02453  02457  02461  02465  02469  02473  02477  02481  02485 

1059  02490  02494  02498  02502  02506  02510  02514  02518  02522  02526 

1060  02531  02535  02539  02543  02547  02551  02555  02559  02563  02567 

1061  02572  02576  02580  02584  02588  02592  02596  02600  02604  02608 

1062  02612  02617  02621  02625  02629  02633  02637  02641  02645  02649 

1063  02653  02657  02661  02666  02670  02674  02678  02682  02686  02690 

1064  02694  02698  02702  02706  02710  02715  02719  02723  02727  02731 

1065  02735  02739  02743  02747  02751  02755  02759  02763  02768  02772 

1066  02776  02780  02784  02788  02792  02796  02800  02804  02808  02812 

1067  02816  02821  02825  02829  02833  02837  02841  02845  02849  02853 

1068  02857  02861  02865  02869  02873  02877  02882  02886  02890  02894 

1069  02898  02902  02906  02910  02914  02918  02922  02926  02930  02934 

1070  02938  02942  02946  02951  02955  02959  02963  02967  02971  02975  4 

1071  02979  02983  02987  02991  02995  02999  03003  03007  03011  03015  o 

1072  03019  03024  03028  03032  03036  03040  03044  03048  03052  03056 

1073  03060  03064  03068  03072  03076  03080  03084  03088  03092  03096 

1074  03100  03104  03109  03113  03117  03121  03125  03129  03133  03137 

1075  03141  03145  03149  03153  03157  03161  03165  03169  03173  03177 
1070  03181  03185  03189  03193  03197  03201  03205  03209  03214  03218 

1077  03222  03226  03230  03234  03238  03242  03246  03250  03254  03258 

1078  03262  03266  03270  03274  03278  03282  03286  03290  03294  03298 

1079  03302  03306  03310  03314  03318  03322  03326  03330  03334  03338 

1080  03342  03346  03350  03354  03358  03362  03366  03371  03375  03379 

1081  03383  03387  03391  03395  03399  03403  03407  03411  03415  03419 

1082  03423  03427  03431  03435  03439  03443  03447  03451  03455  03459 

1083  03463  03467  03471  03475  03479  03483  03487  03491  03495  03499 

1084  03503  03507  03511  03515  03519  03523  03527  03531  03535  03539 

1085  03543  03547  03551  03555  03559  03563  03567  03571  03575  03579 

1086  03583  03587  03591  03595  03599  03603  03607  03611  03615  03619 

1087  03623  03627  03631  03635  03639  03643  03647  03651  03655  03659 

1088  03663  03667  03671  03675  03679  03683  03687  03691  03695  03099 

1089  03703  03707  03711  03715  03719  03723  03727  03731  03735  03739 

1090  03743  03747  03751  03755  03759  03763  03767  03771  03775  03778 

1091  03782  03786  03790  03794  03798  03802  03806  03810  03814  03818 

1092  03822  03826  03830  03834  03838  03842  03846  03850  03854  03858 

1093  03862  03866  03870  03874  03878  03882  03886  03890  03894  03898 

1094  03902  03906  03910  03914  03918  03922  03926  03930  03933  03937 

1095  03941  03945  03949  03953  03957  03961  03965  03969  03973  03977 

1096  03981  03985  03989  03993  03997  04001  04005  04009  04013  04017 

1097  04021  04025  04029  04033  04036  04040  04044  04048  04052  04056 

1098  04060  04064  04068  04072  04076  04080  04084  04088  04092  04096 

1099  04100  04104  04108  04112  04116  04120  04123  04127  04131  04135 

1100  04139  04143  04147  04151  04155  04159  04163  04167  04171  04175 


842 


Probability  of  Errors.  Table  7. 


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Table  8.  Properties  of  Elementary  Substances.  843 


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Properties  of  Solids. 


Table  9a, 


Name 

Symbol 

>> 

1 

<u 

O 

1  Hardness 

Coefficient 
Expansion 
cubic,  o—  100°  1 

3* 
P 

M° 

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„  Acetic  .    .    . 
„  Oxalic  .    .    . 
„  Phosphoric  . 
„  Phosphorous 
»      »      Hypo- 
„  Sulphuric  (hyd.) 
„  Tartaric    .    . 
Arsenate  of 
„  Lead.   .    .    . 
„  Potassium     . 
„     „    (anhyd.) 
Borate  of 
„  Lead    .    .    . 
„      „      Bi-.    . 
„  Potassium     . 
„      „      Bi-.    . 
„  Sodium    .    . 
„      „      Bi-.    . 
„  (Borax)     .    . 
Bromide  of 
„  Lead     .    .    . 
„  Potassium     . 
„  Silver   .    .    . 
Carbonate  of 
„  Barium     .    . 
„  Calcium   .    . 
„  Iron      .    .    . 
„  Lead    .    .    . 
„  Potassium     . 
„  Sodium    .    . 
„      „      (acid)  . 
„  Strontium     . 
Chloral  .... 
Chlorate  of 
„  Barium     .    . 
„  Potassium     . 
„      „      Per-    . 
„  Sodium     .    . 
Chloride  of 
„  Ammonium. 
„  Barium     .    . 
»  ^  >i  (Crystals) 
„  Calcium   .    . 
„      „  (crystals) 
„  Carbon     .    . 
„  Copper 
„  Iron      .    , 

HC2H302.   .   . 
H2C204.2H20. 
H3PO4    .   .   .   . 

i.i 
6 

. 

16 

117 

.46 

44 

100 
12 

IOO 
58 

0 

70 

o 

°+ 

sol 
sol 
47 
4 

7 

0? 

39 
o 

0 
0 
0 
0 

51 

20 

9 

0 

sol 

29 

7 
50 

27 
26 
3i 
42 
83 

<H- 

0 

A7 

IOO 

90? 

IOO 

IOO 
IOO 
IOO 

77 
o 

sol 

36 

67 

o-f 

51 

0 
0 

o 
o 
o 

62 

33 
o 

59 

38 

70 

42 

37 
44 
60 

IOO 

• 

40 
72 

17 

10 

135 

600 

500 
700 
430 

8^0 
850 

50 

400 
350 
600 
300 

sub 

97 
400 

.32 
.29 

.073 
.175 
.156 

.090 
.114 

.205 

.220 
•257 
.233 
.385 

•053 
•113 

.074 

.no 

.210 

•193 
.079 
.211 
.26 

.148 

•157 
.20 
.19 

•38 
.OgO 
.171 

.164 

•4+ 

.2 
.138 

26 

37 
36 

33 
40 

H3P03   .   .   .   . 
H3PO2    .   .   .   . 
H2S04.H20.   . 
H2C4H406    .   . 

Pb3As2O8  .   .   . 
KH2AsO4  .   .   . 
KAsO3  .   .   .   . 

•7 

.8 
.8 

2.9 

PbB2O4  . 

PbB4O7 

1+ 

4 

2  — 

.OOOI26 
.000104 

.000188 

KB02  
K2B4O7  .... 

• 

NaBO2   .   .   .   . 

Na2B4O7    .   .   . 
Na2B4O7.  ioH2O 

PbBr2  . 

2.4 
1-7 

6.6 

7  7 

KBr    

AgBr  

BaCO3    .   . 
CaCO3    .... 
FeC03    .... 
PbC03   . 
K2C03    . 
Na2CO3  . 
NaHCO3 
SrC03    . 
C2H3C1202       . 

BaCl206.H20. 
KC103    .... 
KC1O4 

6-3 

4-3 

2.7 

3-8 
6-5 
2-3 

2-5 

2.2 

3-6 
1.8 

3-2 

2-3 

->  c 

NaC103.   .   .  . 
H4NC1    . 

2.3 

T  r 

BaCl2  

3  8 

BaCl2.2H2O. 

7  n 

CaCl2  
CaCl2.6H2O.   . 
C2C16.   .   .   .   . 
Cu2Cl2    .   .   .   . 
FeClo. 

2.2 

1.6 

2.0 
3-5 

2.S 

• 

0006 

720 
29 
187 
434 

300 

187 

1000 

Table  9a. 


Chemical  Materials. 


849 


Name 

Symbol 

c 
& 

Hardness 

Coefficient 
Expansion 
Cubic  o—ioo° 

bo., 

.S.G 

!? 

'o 

PH 

Specific 
Heat  0—100°  || 

If 

rj 

£!.S 

"-So 

1! 

Chloride  of 

„  Lithium    .    . 
„  Magnesium  . 
„  Mercury  .     . 
,,    „  (calomel) 
„  Potassium    . 
„  &  platinum  . 
„  Rubidium     . 
„  Silver   .    .    . 
„  Sodium    .    . 
„  Strontium     . 
„  Tin  .... 
„    „    (crystals) 
„  Zinc     .    .    . 
Chromate  of 
,,Lead  ..    .    . 
„  Potassium     . 

„  Sodium    .    . 
„    „  Bi-  .    .    . 
Cyanide  of 
,,  Mercury  .    . 
„  Potassium     . 
„    „  Ferri-.    . 
„    „  Ferro  .    . 
Fluoride  of 
,,  Calcium   .    . 
Hyposulphite  of 
„  Barium     .    . 
„  Lead    .    .    . 
„  Potassium    . 
„  Sodium    .    . 
,,    .,    (crystals) 
Iodide  of 
„  Copper    .    . 
,,Lead    .    .    . 
„  Mercury  .    . 
„  ,,(mercurous) 
„  Potassium    . 
„  Silver   .    .    . 
„  Sodium     .    . 
Naphthalene 
Nitrate  of 
„  Ammonium. 
„  Barium     .    . 
,,Lead  ..    .    . 
„  Potassium    . 

PbCl2  . 

c  8 

2 

.000114 

.00010 
.000121 

6OO 

700 
290 

730 
450 

775 
850 
250 

900 

300 

625 

.067 

.282 
.194 

.067 

.052 

.172 

.112 
.09I 
.214 
.120 
.IO2 

• 

i 

45 
70? 

7 
o 
26 

i 

0 

27 

35 

67? 
80? 
80 

o 

39 
ii 

60? 

12 

30 
25 

O 

o+ 
sol 

41 

64 

O.I 

5? 
o 

59 

0 

64 
o 

T 

36 

24 

5 
57 

35 

36 

5 

o 

28 
50 

45 
50 

35 

55 
44 
50 

o 

100 

o.5 

67? 
o 

76 
26 

LiCl  ...... 
MgCls  .... 
HeCl2  .... 

$SP.  :  :  : 

2.0 

2.2 

54 
I-1 

->  o 

3.5 

AsCl 

•*  6 

NaCl 

^  T 

SrCl2  .... 

?  O 

SnCl3.2HaO  . 
ZnCl2  .... 

PbCr04  .  .  i. 
K2Cr04  .  .  . 
K2Cr2O7  .  ,.  . 
NazCrO4.  '.  . 
Na3Cr2O7  ... 

1  7 

2.8 

5-9 

2-7 

2-7 
2.7 

4.0 

T  C 

_ 

•  • 

260 

700 

.136 

!i8y 
.188 

.100 

•233 
•>8o 

• 

K6Fe3Ci3Ni2  . 
K4FeC6N5.3H20 

CaFa 

1.8 
1-9 

?  ^ 

4 

.00004? 

900 

• 

.212 

anh. 
.163 

• 

BaS2O3.H3O  . 
PbS2O3  .  .  . 
K2S2O3  .  .  . 

34 

• 

.00013 
.000101 

30? 

600 
380 
250 
290 
640 
530 
630 
80 

I  CQ 

600 
34° 

760 
900 
350 
3IO 

215 

.092 
.197 
.221 

445 

,069 

.043 
.042 

.039 
.082 
.062 
.088 

455 
.150 
.114 
•235 

.33 

36 
49 

Na3S3O8  .  .  . 
Na3S2O3.5H2O 

Cu2I2  .  .  .  . 
Pbl,  . 

1-7 

tt 

• 

HgI2  .... 

6  T 

• 

.000072 

.000128 
—.000004 

•     » 

9-7 
3-1 

C  -7 

Nal 

T  ^ 

H4NNO3  .  .  . 
BaN«06  .  .  . 
PbNo06  .  .  . 
KN03  .... 

1.7 

3-2 

44 

2.1 

2 

850 


Properties  of  Solids. 


Table  9a. 


Name 

Symbol 

>, 
1 

6 
Q 

Hardness 

Coefficient 
Expansion 
Cubic  o—ioo° 

M  ., 

S  c 

P 

t! 
sl 

Specific 
Heat  0—100° 

• 

«  M 

-i  C 

w 

J 

^ 
>«- 

f! 

">* 

^ 

lEc 

K 

Nitrate  of 

„  Silver  .    .    . 
„  Sodium    .    . 
„  Strontium    . 
Oxalate  of 
„  Potassium    . 
„    „  Tetr-  .    . 
Oxide  of 
„  Aluminum   . 
„  Antimony    . 
„  Arsenic    .    . 
„  Bismuth  .    . 
„  Boron  .    .    . 
„  Calcium  .    . 
„        (hydrate) 
„  Chromium 
„  Copper    .    . 
„    „  (cuprous) 
„  Iron     .    .    . 

"  kead    '•   '    ' 
„  Magnesium  . 

„         (hydrate) 
„  Manganese   . 

"  *r  Pei"   '    ' 
„  Mercury  .    . 

„  Molybdenum 
„  Nitrogen  .    . 
„  Potassium    . 
„        (hydrate) 
„  Silicon     .    . 

AsNO« 

1  ? 

7TO 

• 

T44 
270 
I8l 

236 
283 

198 

093 

.128 
.061 
.237 

6*5 

7° 
47 
42 

25 
5  ' 

o 
o-h 

2 
0 
2 

.1  + 

90 
64 

50 

40 

o 

0+ 
8? 

.1— 

O.I 
.      1 

o 

0 

o 
o 

04 

O.I 

0 

70 

o 

25 

0 
0 
0 

NfNo33  :  :  . 

SrN2O6     .     .     . 

K2C204.H20     . 
KH3C408.2H2O. 

A1303  .... 
Sb2O3            .     . 

2.2 
2.9 

3-9 

2  — 
9 

310 
650 

ASoOa 

?  7 

Bi203  .... 
BoOq    . 

8.1 
T  8 

• 

.  . 

5^0 

• 

7-2X3 
CaO     .... 

CaO2H2    .     .     . 

3-1 

?  T 

• 

Cr2O3  .... 
CuO     .... 
Cu2O         .     .     . 

5-0 
64 
60 

. 

. 

.177 
•  !35 

. 

0 
0 

o 

0 

o+ 

0 

o+ 
o 

0 

0 
0.2 

FeoO«  . 

C  "> 

5+ 

.00004 

' 

. 

.16 
.051 
.244 
.312 

PbO     .... 
MgO    .... 
MeO9H«   . 

9-3 
3-3 

MnO    .... 
MnO3  .... 
HsO 

5-i 

5-0 

TT 

H- 

. 

• 

•157 
•159 

MoO3        .     .     . 

NoOs 

.00004 

30 

47 

.19 

77 

80? 
50 
67 

o 

40- 

60 

0 
0 

o 

0 

(?), 

0-f- 
0 

sol 
sol 

5 
20 

0 
0 

o 

K20     .     .     .     . 
KOH   .... 
SiO2     .... 

2.6 
2.0 

7  i 

. 

Na2O  .... 

„    ,,  (hydrate) 
„  Tin  .    .    .    . 
„  Titanium.    . 
„  Tungsten.    . 
„  Zinc     .    .    . 
Phosphate  of 
„  Calcium  .    . 
„  Lead    .    .    . 
„  Potassium    . 
„    „  (acid)  . 
„  Sodium    .    . 
„    „  (acid).    . 
Silicate  of 
„  Al  etc.  (clay) 
„  Calcium  .    . 
„  Zirconium   . 

NaOH.     .     .     . 

?.  T 

SnO2    ....  !6.o 

6+ 

.00002 
.00003 

§ 

• 

.091 
.172 
.085 
.125 

.199 
.082 
.191 
.208 
.228 
•454 

•*+ 
.178 

.132 

' 

: 
• 

Ti02    .... 
WO3    .... 
ZnO     .... 

4- 
6.8 

'  7 

CaP2O6    .     -     . 
Pb2P2O7 

. 

. 

• 

K4P207     .     .     . 
KH2PO4  .     .     . 
Na4P207  .     .     . 
Na2HP04.i2H20 

Al2Si2O7.2H2O,etc. 
CaSiO«     .     .  "    . 

2-3 

2.4 

1.5 

2. 

1  ; 

• 

.00002? 

900 
36 

• 

ZrSi04      .     .     . 

7-f 

• 

. 

Table  9a 


Chemical  Materials. 


851 


Name 

Symbol 

en 
C 
<u 

Q 

Hardness 

Coefficient 
Expansion 
cubic.  o—ioo° 

Sc 
P 

i 

sT 

C/5  S 

la 
P 

1 

o 

1 

Sulphate  of 

„  Ammonium. 
Barium 

(H4N)2S04    .  .  .   . 
BaSO4    

1.8 
/I  4 

.OOOO6 

140 

•350 
.TTO 

. 

43 
o 

50 

0 

Calcium   . 

3.0 

3 

.in 

0.2 

o,? 

„      ,    (hydrat.) 
Cobalt 

CaSol.2H2O  .   . 
CoSO4  7H2O  .   . 

2-3 
T  n 

2  — 

• 

• 

.26 
.•242 

• 

O.2 

18 

O.2 

„  Copper    .    . 
„      „  (crystals) 
„  Iron     .    .    . 

„  Magnesium  . 
„      „  (hydrat.) 
Manganese 

CuSO4    
CuSO4.sH2O  .   . 
FeSO4.7H2O  .   . 
PbS04    
MgS04   
MgSO4.7H2O  .   . 
MnSO4  .       ... 

'J 

3-6 

2-3 

1.9 
6-3 

2.7 

?  n 

2+ 
2 

• 

• 

.184 
•30 

•350 
.083 
.225 
.38 
18 

• 

19 

30 

50 
0 
26 

55 

43 

67 

80 
o 
40 

87 

"  Nickel^  rf'. 
„      „  (hydrat.) 
„  Potassium    . 

MnSO4.5H2O  .   . 
NiS04!  
NiS04.7H2O   .  . 
K2S04    
KHSO4  

2.1 

2.0 

2.6 

: 

TIC 

• 

•33 
.216 

.341 
.193 

.244 

• 

50 
28 

52 

10 

37, 

21 

„       „  &  Al  (alum) 
Sodium 

K2A12S4O16.24H2O 
K2Cr2S4O16.24H2O 
Na2SO4      

i!s 

1  7 

2+ 

QOO 

. 

.371 
.324 
.2^0 

• 

13 
H 

30? 

t 

(crystals^ 

Na2SO4.ioH2O   .   . 

. 

60? 

,,  Strontium 

SrSO4     

7  7 

.00006 

.140 

0 

o 

„  Zinc     .    .    . 
„      „  (hydrat.) 
Sulphide  of 

,,  Antimony 

ZnSO4    
ZnSO4.7H2O  .   .   . 

SbS3       

3-5 

2.0 
1   r 

2+ 

• 

• 

.174 

•34 
.084 

• 

35 
62 

0 

« 

,,  Bismuth  . 

,060 

0 

CoDDer 

CuS 

o 

„     „  (cuprous) 
„     „  &  iron     . 

Cu2S  
CuFeS2  
FeS 

*'" 

5'^ 

3— 
4— 

. 

. 

.121 
*T?6 

• 

0 

o 

0 

Rl-      '    ' 

r.  o 

6-|- 

.00003 

T?,8 

0 

'      T       '         1 

„  Lead    . 

PbS 

7    C 

.00007 

.050 

o 

"   TV 

.    Mercury 

HeS    . 

2-t 

°5T 

o 

i    Nickel. 
.   Potassium 

K2S'.   .'.'..... 

4.6 

">  T 

• 

• 

• 

.128 

• 

o 

50? 

,   Silver  . 

7  0 

2-4- 

071; 

o 

,   Tin  .    . 
,       „  Bi- 
,,  Zinc 

SnS2   '.   '.  '.   .   .       '. 
ZnS    ... 

5-0 

4-5 

1    T 

4  — 

.000036 

. 

. 

.084 
.119 

.122 

. 

o 
o 
o 

Talc  

1   7 

1 

o 

Tartrate  of  .    . 

,,  Potass,  (acid) 

KHC4H4O6  . 

06 

6 

„     „  &  sodium 

KNaC,  "-i4O6.4H2O 

. 

•• 

50 

• 

•33 

• 

50? 

852 


Properties  of  Solids.  Table  10. 


q  '  o 


jo 


XjBUIpJQ  JO 


jo  xapui 


: 
r        ro 


XjISUSQ 


I—      M    VO     «     l-<      NM 


o* 


ti 


•  • 


Q     UUU 


Table  10. 


Optical  Materials,  etc. 


853 


JHx:  O  >>     -xi  C"c>        rt       -       • 
UUUU     QWWfc^O      O 


854 


Properties  of  Soilds. 


Table  10, 


UOlSjgdSIQ 

jo  xapui 


umuiixB^i 
jo  xapuj 


(Q) 


jo 


onpuj 


AiAipnp 
-uo'3  JBSH 


jo 


0OOI-,yO 

IB3H 


uio  gL 
'luioj  Sunjog 


juioj  Saiip^j 


Oooi-0o 
uoisiiBdxg 


sssupaBH 


S.5 


^•s, 


O  VO 

•o    •    •  o 

•5VO       •       •    m 


if)     •      «    <y-  f) 

\r>    •     •^•*     *     .»'> 


ft<ONrJ->->{SvOO  ^-       o-i 

OO    'O  C\  t^OO   OOO      .   ^>  «^^-  vr> 


ON    .  .  N 

t  :  :  :-? 


ro  •      :  N 


CO 

2 

en 

c 
-o 


O 
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NO 


1 


r^      r-^  o       w>      r^ 

•-    ^-  O  \O    &00   C<    ^-  O   N    OOO  vc   LD  O      •  N 


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o 

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• 


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o-H 

3 

a* 


IS 


rtJ3-J.  0)l>OO3c3<U 
Q,!1HO/^^;^^O^MCA1  A 


Table  10. 


H-V 

UOISJ3USIQ  JO 


jo  xapuj 


-10 


(Q) 


Optical  Materials,  etc.    •.          855 


:::::::  :^3  ::::: 


OO       •    ^-  h-i  VO    PO  inoo 


%'• 


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jo  xapuj 


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uio  gL 
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856 


Properties  of  Liquids.  Table  11. 


•H-V 

tioisjadsiQ 
jo  xapuj 


(a) 


jo 


Dnpupoa 


BO 

adg 


0OOI— ,0 
'JB3R 


(0OS)JOdBA 


"o 


I^vo     .  iovo 


t^  r^  t^oo 


q  q    *  q  q  q  q  q  q  q  q    *  q  q    '  q  q  q  q  q  q  q 

rO     *  ro  "3"     *   rj-  Tj-  vn  ro  c*y  fO  fO 


w   «  w    » N*-'  ^  '"i-*  "*  .  *j' i-r*  •  *^  r  •       •    • 


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?  -    -     3 


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Satitog 


»n!°c[ 

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uoisuBdxg 


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o'  o'  o'  o'  o'  o  i-i  i-T  o'  o'  i-T  ~  ~  HH*  o'  o  o'  »-»*  o'  o*  o*  o  .  r2 


O  O          rO\O    O    t^ 
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o  a-oo       oo  o    o    oo 


o||fi|lll|g  ;|5:|og§gg§ 


>, 

C  Z* 


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Tabiejt          Properties  of  Liquids. 


857 


H-y 

aoisj8dst( 
jo'xgpuj 


(a) 

joBjj 

JO  X3pUJ 


-no  3  JBSJJ 


UIlBZUOd 
-BA 


«poi-0o 

'JB3H 

ode 


J° 


guiipe 


8UIZ99JJ 


00  JTJ 

uoistiBdxg 


jo  S 


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Table  11. 


Properties   of  Liquids. 


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Table  11 


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Table  12.    Properties  of  Gases  and  Vapors.     861 


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Table  12.    Properties  of  Gases  and  Vapors.     863 


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Tables  13  C-D. 

13  D.  Density  of  Steam  saturated  at  Difterent  Ternperalures. 

Temperature.  .0°  10  20  30  40  50  60  70  80  90  100° 
Density  000005  .000009  .000017  .000030  .000051  .000083  .000131  .000199  .000296  .000428  .000606, 

Temperature.  .  100°  no  120  130  140  150  160  170  180  190  200° 
Density.  .  .  .  .000606  .00:840  .00114  .00153  .00201  .00260  .00333  00421  .00526  .00650  .00796 

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Tables  U-14A.       Aqueous  Vapor.  867 


14    Boiling  Points  of  Water 

cm.         .0          .1           .2          .3 
<L>  68     96.92    96.96    97.00    97.05 
g  69    97-33    97.36    97.40    97.44 
8  7°    9772   9776    97-8o   97-84 
£  71     98.11    98.15    98.19    98.23 
y  72     98.50   98.54    98.58    98.61 
"C  73    98.88   98.92   98.96   98.99 
|  74     99  26   99.30   09.33    99.37 
5  75    99-63   99.67   99-71    99.74 

at  Different  Pressures  (g  = 

.4          .5          .6          .7 
97.09    97.13    97.17    97.21 
97.48    97.52    97.56    97.60 
97.88    97.92    97.96    98.00 
98.27    98.31    98.34    98.38 
98.65    98.69    98.73    98.77 
99.03    99.07    99.11    99.14 
99.41    99.44    99.48    99.52 
99.78    99.82    99.85    99.89 

980-61) 

.8 

97-25 
97.64 
98.03 
98.42 
98.80 
99.18 
99.56 
99-93 

•9 
97.29 
97.68 
98.07 
98.46 
98.84 
99.22 

99-59 
99.96 

76  mo  oo  100.04  100.07  100.1  1  100.15  100.18  100.22  100.26  100.29  100.33 

ffl  77  100.36  100.40  100.44  100.47  100.51  100.55  100.58  100.62  100.65  100.69 

14A.   Dew  Points  corresponding  to  Different  Degrees  of  Tern  perature 
and  Relative  Humidity. 

Relative  Humidity  of  the  Air. 

loO/o   2oO/0    30%   40%    50%    60%    700/0  80%  900/0  100% 

o°       ..         ..      —  16    —  12     —  9     —  7     —5  —  3  —  i  o° 

1  ..        ..          1511         8         6         4  2  o  4  i 

2  ..      —19        14       10         7         5         3  —i  +i  2 

3  18        13          9          6          4          2  o  2  3 
,4°       ••      —17    —12     —8     —6     -3     —  i  +i  43  +4 

5°.     ..  •  —  16    -ii     —7     —5     —  2         o  4-2  43  4-5° 

6                     15        10         7          4     —i     4i  3  4  6 
7..          i5963°2457 

8                     14—9          5          2     4i          3  5  6 

9°       ..      —13     —8     -4     -i     +2     44  +6  4-7  49° 

,    10°      ..     —12     —7     —3         o     43     4-5  4-7  4~8  +">° 

.!:    ii                    ii          6         2     -J-i          3          6  8  9  ii 

<    12      —  19       10         5     —  i          2         4         7  9  10  12 

«,    13          18       10         4         o         3          5          8  10  ii  13 

^     I4o     _I?    _9     _3     +!     4.4     _|_6     49  +11  +12  4H° 

<!   15°   —17   —8    —3    4-2    4-5    4-7  4-io  412  4-13  4*5° 

o  16    16    7    2    2    6    8    ii  13  14  16 

«  17    15    6—1    3    6    9    ii  14  15  J7 

i*  18    14    5    o    4    7   10   12  14  16  18 

a  19°  —13  —5  4  1  4-5  48  411  4-13  4i5  +17  +19° 

*   20°   —13   —4    4-2    4-6    49  4-12  414  416  4-18  420° 

<u  2i     12    3    3    7    10    13    15  17  T9  21 

&*  22      II      2      4      8     II     14     16  18  20  22 

6  23    -io  —i    4    9    12   15    17  19  21  23 

«  24°  —io    o  45  410  413  +16  4i8  420  422  424° 

250       _9             04-6     4-10     4l4     417      4-19  421  4-23  +2S° 

26  84-1    7   ii   15   18   20  22  24  26 

27  7    2    8   12   16   19   21  23  25  27 

28  7    3    9   13   17   20   22  24  26  28 
29°  —6  4-4  4io  414  418  420  423  425  427  429° 


30° 

_5 

4-5 

4n 

+15 

4-i8 

+21 

4-24 

4-26 

4-28 

430° 

3i 

4 

5 

ii 

16 

19 

22 

25 

27 

29 

3i 

32 

3 

6 

12 

17 

20 

23 

26 

28 

30 

32 

33 

3 

7 

13 

18 

21 

24 

27 

29 

31 

33 

34 

2 

8 

M 

18 

22 

25 

28 

30 

32 

34 

35° 

—  I 

+  9 

+15 

419 

+23 

426 

+2Q 

+31 

433 

435° 

868 


Aqueous  Vapor. 


Tables  15, 15  A. 


15.  Hygrometric  Table,  showing  at  a  given  temperature  (T),  the  maximum 
pressure  (P)  of  aqueous  vapor  in  mercurial  centimetres,  the  maximum  density 
(D)  of  aqueous  vapor,  and  the  factor  (F)  by  which  the  difference  between  a  wet 
and  a  dry  bulb  thermometer  must  be  multiplied  to  find  the  difference  between 
the  dew-point  and  the  temperature  (T)  of  the  air. 


T 

P 

D 

F 

T 

P 

D 

F 

-10° 

0.22 

.OOO0023 

8.8 

4-10° 

0.9! 

.0000093 

2.1 

-9 

•23 

25 

8.5 

11 

0.98 

.OOOO  1  00 

2.0 

-8 

•25 

27 

8.2 

12 

.04 

1  06 

2.0 

-7 

.27 

29 

7-9 

13 

.11 

112 

2.0 

-6 

.29 

32 

7.6 

M 

.19 

120 

1.9 

-5° 

0.32 

.0000034 

7-3 

+15° 

•27 

.OOOOI28 

1.9 

— 

-4 

•34 

37 

6.8 

16 

•35 

135 

.9 

-3 

•37 

40 

6.0 

17 

.44 

144 

•9 

-2 

•39 

42 

5-0 

18 

•53 

152 

.8 

-I 

.42 

45 

4.1 

'9 

•63 

162 

.8 

0° 

0.46 

.0000049 

3-3 

+20° 

•74 

.0000172 

.8 

-I 

.49 

52 

2.9 

21 

.85 

182 

.8 

-2 

•53 

56 

26 

22 

.96 

'93 

•7 

-3 

60 

2.5 

23 

2.09 

204 

•7 

-4 

.61 

64 

2.4 

24 

2.21 

216 

7 

-5° 

0.65 

.0000068 

2.3 

+25° 

2.35 

.0000229 

•7 

-6 

.70 

73 

2.2 

26 

2.50 

242 

•7 

-7 

•75 

77 

2.2 

27 

2.6S 

256 

•7 

-8 

.80 

82 

2.1 

28 

2.81 

270 

i-7 

-9 

.85 

87 

2.1 

29 

2.97 

285 

i.7 

10° 

.ql 

.0000093 

2.T 

+30° 

3.15 

.0000301 

1.6 

15  A.  Specific  Heat  of  Moist  Air  under  Constant  Pressure  (76  cm.) 


Dew- 
Point 

Specific 
Heat. 

Dew- 

Point 

Specific 
Heat. 

Dew- 
Point. 

Specific 
Heat. 

—  cc° 

.2383 

—11° 

.2387 

+12° 

.2404 

—33 

.2383 

—  10 

.2387 

13 

.2405 

—32 

.2384 

—  9 

.2388 

H 

.2407 

—3i 

.2384 

—  8 

.2388 

15 

.2408 

—30 

.2384 

—  7 

.2388 

16 

.2410 

—29 

.2384 

-  6 

.2389 

17 

.2412 

—28 

.2384 

c 

.2389 

18 

.2414 

—27 

.2384 

-  4 

.2390 

19 

.2416 

-26 

.2384 

3 

.2390 

20 

2418 

—25 

.2384 

—  2 

•2391 

21 

.2420 

-24 

.2384 

—  I 

.2392 

22 

.2423 

--23 

.2384 

O 

.2392 

23 

—  22 

.2385 

+  I 

•2393 

24 

.2428 

—  21 

.2385 

2 

•2394 

25 

.2430 

—  2O 

.2385 

3 

•2394 

26 

.2433 

—  I9 

.2285 

4 

•239$ 

27 

.2436 

—  18 

.2385 

5 

.2396 

28 

.2440  - 

-17 

.238^ 

6 

•  2397 

2Q 

.2443 

—  16 

.2386 

7 

.2398 

30 

.2447 

-15 

.2386 

8 

.2399 

31 

.2451 

—14 

.2386 

Q 

.2400 

32 

•24=0 

—13 

.2386 

10 

.2401 

33 

•2459 

-12<> 

.2387 

11° 

.2403 

100° 

.4805 

Tables  15,  B  — C.         Aqueous  Vapor. 


869 


15,  B     Velocity  of  Sound  in  centimetres  per  second  through  Atmospheric 
Air  at  Different  Temperatures  and  under  Different  Conditions  of  Relative 

Humidity. 


Re- 
lative 
Hu- 
midity 

o% 

200/o 

40% 

60  o/o 

800/0 

TOO  O/o 

0° 

33,220 

33,225 

33,231 

33,236. 

33,242 

33,247 

1° 

33,281 

33,286 

33,292 

33,298 

33,304 

33,310 

2° 

33,34* 

33,347 

33,353 

33,360 

33,367 

33,373 

3° 

33,402 

33,408 

33,415 

33,422 

33,429 

33,436 

4° 

33,462 

33,469 

33,476 

33,484 

33,491 

33,499 

5° 

33,523 

33,530 

33,538 

33,546 

33,554 

33,562 

6° 

33,583 

33,591 

33,6oo 

33,608 

33,6i7 

33,625 

7° 

33,643 

33,652 

33,66i 

33,670 

33,679 

33,689 

8° 

33,703 

33,713 

33,722 

33,732 

33,742 

33,752 

c  9° 

33,763 

33,773 

33,784 

33,794 

33,805 

33,815 

•-  10° 

33,823 

33,834 

33,845 

33,856 

33,867 

33,879 

<  11° 

33,882 

33,894 

33,906 

33,9  T  8 

33,930 

33,942 

CD    12? 

33,942 

33,955 

33,()67 

33,98o 

33,993 

34,006 

•5  I3o 

34,001 

34,oi5 

34,029 

34,043 

34,056 

34,070 

34,060 

34,075 

34,090 

34,105 

34,TI9 

34,134 

o  15° 

34,120 

34,^6 

34,151 

34,167 

34,183 

34,T98 

o>  16° 

34,179 

34,196 

34,2J3 

34,229 

34,246 

34,263 

»-  17° 

34,238 

34,256 

34,274 

34,292 

34,310 

34,328 

3   jgo 

34,297 

34,3i6 

34,335 

34,354 

34,374 

34,393 

«  19° 

34,356 

34.376 

34,397 

34,417 

34,438 

34,458 

S  20° 

34,415 

34,436 

34,458 

34,480 

34,502 

34,524 

OH  21° 

34,474 

34,496 

34,520 

34,543 

34,566 

34,589 

E   22° 

34,532 

34,557 

34,58i 

34,606 

34,630 

34,655 

023° 

34,590 

34,6i7 

34,643 

34,669 

34,695 

34,722 

H24° 

34,649 

34,677 

34,705 

34,732 

34,76i 

34,789 

25° 

34,707 

34J37 

34,766 

34,796 

34,826 

34,856 

26° 

34,765 

34,797 

34,828 

34,86o 

34,892 

34,924 

27° 

34,823 

34,857 

34,890 

34,924 

34,958 

34,992 

28° 

34,881 

34,917 

34,953 

34,988 

35,025 

35,061 

29° 

34,939 

34,977 

35,OI5 

35,053 

35,092 

35,130 

30° 

34,997 

35,037 

35,077 

3^118 

35,158 

35,T99 

31° 

35,05  S 

35,097 

35,139 

3^,182 

35,225 

35,269 

32° 

35,IT3 

35,157 

35,202 

35,247 

35,293 

35,340 

33° 

35,170 

35,265 

35,313 

35,362 

35,412 

15,  C.    Coefficients  of  Interdiffusion  of  Gases.   (C.  G.  SO* 


Air 

Car- 
bonic 
Oxide 

Hy- 
drogen 

Meth- 
ane 

Nitrous 
Oxide 

Oxygen 

Sulphur- 
ous An- 
il I'dride 

CO 

H, 

CH4 

N2O 

9 

soa 

Carbonic 

Dioxide  C  O2 

.1423 

•5614 

.1586 

.0982 

.1409 

Hydrogen     H  2 

.6422 

.7214 

.4800 

Oxygen  Os  .  . 

.1802 

.7214 

*  See  Maxwell's  Theory  of  Heat,  4th  Ed.  page  332.    (Everett  Art.  131.) 


870  Barometric  Tables.  Table  16. 

REDUCTION  or  INCHES  TO  CENTIMETRES. 


Inches. 

o 

i 

2 

3 

4 

5 

6 

7 

8 

9 

28.0 

71.119 

•145 

.170 

.196 

.221 

.246 

.272 

•297 

•323 

•348 

28.1 

71-373 

•399 

•424 

•450 

•475 

.500 

•526 

•551 

•577 

.602 

28.2 
28.3 

71.627 
71.881 

•653 
•907 

.678 
•932 

.704 
•958 

.729 
•983 

•754 
*oo8 

.780 
"•034 

•805 
*059 

% 

.856 

*IIO 

28.4 

72.135 

.161 

.186 

.212 

-37 

.262 

.288 

•339 

•364 

28.5 

72-389 

•415 

•44° 

.466 

.491 

.516 

•542 

ii 

•593 

.618 

28.6 

72-643 

.669 

•694 

.720 

•745 

.770 

•796 

.847 

.872 

28.7 

72.897 

•923 

.948 

•974 

•999 

*024 

•"050 

*°75 

*IOI 

*I26 

28.8 

73.151 

.177 

.202 

.228 

•253 

.278 

•304 

•329 

•355 

.380 

28.9 

73-405 

•431 

•456 

.482 

•507 

.532 

•558 

•583 

.609 

•634 

29.0 

73-659 

•685 

.710 

•736 

£61 

.786 

.812 

•837 

•863 

.888 

29.I 

•939 

•964 

.990 

*O4O 

*o66 

'091 

*n7 

*I42 

29.2 

74.167 

•193 

.218 

•244 

.269 

•294 

.320 

•345 

•371 

.396 

29-3 

74.421 

•447 

.472 

•498 

•523 

.548 

•574 

•599 

•625 

.650 

29-4 

.701 

.726 

•752 

•777 

.802 

.828 

•853 

•879 

•904 

29-5 

74.929 

•955 

.980 

*oo6 

"031 

'056 

*o82 

*i33 

*i5S 

29.6 

.209 

•234 

.260 

•285 

.310 

•336 

•36? 

•387 

.412 

29.7 

75-437 

•463 

.488 

•5I4 

•539 

•564 

•590 

•615 

.641 

.666 

29.8 

75-69I 

.717 

.742 

.768 

•793 

.818 

.844 

.869 

;895 

.920 

29.9 

75-945 

.971 

•996 

*022 

*047 

"072 

'098 

-123 

*i74 

30.0 

76.199 

.225 

.250 

.276 

.301 

•326 

•352 

•377 

•403 

.428 

30.1 

76.453 

•479 

•504 

•530 

•555 

.580 

.606 

.631 

•657 

.682 

30.2 

76.707 

•733 

•758 

.809 

•834 

.860 

•885 

.911 

;93<s 

30.3 

76.961 

•987 

*OI2 

*O38 

*o63 

*o88 

*n4 

*I39 

"165 

30-4 
30.5 

77-215 
77-469 

.241 
•495 

.266 
•520 

.292 
•546 

•571 

•342 
•596 

-368 
.622 

•647 

.419 
•673 

•444 
.698 

30.6 

•749 

•774 

.800 

.825 

.850 

.876 

.901 

•927 

•952 

30.7 

77-977 

*003 

*028 

""053 

"079 

*io4 

*i3o 

*i8o 

*206 

30.8 

78.231 

•257 

.282 

•307 

•333 

•358 

-384 

.409 

•434 

.460 

30.9 

78.485 

•536 

•561 

•587 

.612 

.638 

•663 

.688 

.714 

31.0 

78.739 

•765 

.790 

•815 

.841 

.866 

.892 

.917 

.942 

.968 

78.993 

"019 

*044 

"•069 

*095 

*I20 

*i46 

•171 

"196 

*222 

31.2 
31-3 

79.247 
79-5oi 

•273 

•527 

.298 

.552 

•323 

•577 

•349 
•603 

•374 
.628 

.400 
-654 

.679 

•450 
.704 

•476 

•73° 

31-4 
31-5 

79-755 
80.009 

.781 
•035 

!o6o 

.831 
.085 

•857 
.in 

.882 
.136 

.908 
.162 

•933 

.187 

•958 

.212 

.238 

h    In. 

.001 

.002 

.003 

.004 

.005 

.006 

.007 

.008 

•009 

.010 

Q  Cm. 

.003 

.005 

.008 

.010 

.013 

.015 

.018 

.020 

.023 

.025 

*  The  star  indicates  that  the  number  of  whole  centimetres  is  to  be  read  from 
the  line  underneath  it. 


Tables  1C  A— 17  B.       Barometric  Tables. 


871 


16  A.  Redaction  of  Mercurial  Centimetres  to  Megadynes  per  sq.cm.  g=980. 
cm  .u   .1    .2    .3    .4   .5    .6    .7    .8    .9  Dif. 

70  0.9327  0.9340  0.9354  0.9367  0.9380  0.9393  0.9407  0.9420  0.9433  0.9447  1M 

71  .9460  .9473  .9487  .9500  .9513  .9527  .9540  .9553  .9567  -9580  i  i 

72  .9593  .9607  .9620  .9633  .9647  .9660  .9673  .9687  .9700  .9713  *  3 

73  .9727  .9740  .9753  .9767  .9780  .9793  .9807  .9820  .9833  .9847  4  I 

74  .9860  .9873  .9886  .9900  .9913  .9926  .9940  .9953  .9966  .9980  5  7 

75  .9993  1.0006  1.0020  1.0033  1.00461.0060  1.0073  1.0086  i.o TOO  1.0113  7  Q 

76  1.0126  1.0140  1.0153  1.0166  1.0180  1.0193  1.0206  1.0220  1.0233  1.0246  g  n 

77  1.0260  1.0273  1.0286  1.0300  1.0313  1.0326  1.0339  T'°353  1.0366  1.0379  9  12 

16B.  Reduction  of  Mercurial  Centimetres  to  Megadynes  per  sq.  cm.  g— 981. 
cm  .0    .1    2    .3    .4    .5    .6    .7    .8    .9  Dif. 

70  0.9336  0.9350  0.9363  0.9376  0.9390  0.9403  0.9416  0.9430  0.9443  0.9456  13J 

71  .9470  .9483  .9496  .9510  .9523  .9536  .9550  .9563  .9576  .9590  i  i 

.9616  .9630  .9643  .9656  .9670  .9683  .9696  .9710  .9723  *  3 

•9777  .9790  -9803  .9817  -9830  .9843  .9857  4  5 
.9910  .9923  .9937  .9950  .9963  .9977  .9990  5  7 
[.0043  1.0057  1.0070  1.0083  1.0097  i.ono  1.0123  °  U 
76  1.0137  1.0150  1.0163  1.0177  1.0190  1.0203  1.0217  1.0230  1.0243  1.0257 


72  .9603 

73  .9737 

74  .9870 

75  1.0003 


.9750  .9763 
.9883  .9897 
:. 00.17  1.0030 


77  1.0270  1.0283  1.0297  1.0310  1.0323  1.0337  T-0350  1.0363  1.0377  1.0390  9 12 


17.  Elevation  in  Metres  above  the  Sea  Level  corresponding  to  Different 

Barometric  Pressures  at  10°  Centigrade  (g-980.6). 

cm   .0 

.1    .2 

.3    .4    .5    .6    .7 

.8    .9 

60  1959 

1945  i93i 

1918  1904  1890  1876  1863 

1849  1836 

61  1822 

1808  1795 

1782  1768  1754  1741  1727 

1714  1701 

62  1687 

1674  1660 

1647   1634   l621   l6°7  T594 

1581  1568 

63  1555 

1541  1528 

1515   1502   1489  1476  1463 

H50  1437 

64  1424 

1411  1398 

1385   1372   I36o  1347  1334 

1321  1308 

65  '1295 

1283  1270 

1257   1245   1232  1219  1207 

1194  1182 

66  1169 

1157  1144 

1131   1119   1107  1094  1082 

1069  1057 

67  1044 

1032   1020 

1007   995   983   971   958 

946   934 

68   922 

9IO    897 

885   873   861   849   837 

825   813 

69   80  1 

789   777 

765   753   74i   729   717 

705   693 

70   68  1 

670   658 

646   634   623   611   599 

587   576 

71   564 

552   54i 

529   517   506   494   483 

471   460 

72   448 

437   425 

414   402   391   379   368 

356   345 

73   334 

322   311 

„  300   288   277   266   255 

243   232 

74    221 

2IO    199 

187   176   165   154   143 

132    121 

75   no 

99    88 

77    66    55    44    33 

22     II 

76    o 

—  II   —22 

—33  —43  —54  —65  —76 

—87   —98 

77  —  108  —  119  —  130 

—141  —151  —162  —173  —183  —194  —205 

78  —  215  —  226  —  236 

—  247  —  258  —  268  —  279  —  289  —  300  —  310 

17  A.  Correction  for  Temperature  in  17. 

17B.  Correction  for  Humidity  in  17. 

Mean  Subtr. 

Mean  Add 

Mean  Add 

Dew-  Add 

Dew-  Add 

Dew-  Add 

Temp.  °/0 

Temp.  % 

Temp.  % 

Point   % 

Point  % 

Point   % 

o°   3-5 

10   0.0 

20   3-5 

—  oo  O.O 

+io  0.5 

+20   0.9 

I     3.2 

II   0.4 

21   3.9 

—20  0.0 

II   0.5 

21   0.9 

2     2.8 

12   0.7 

22   4.2 

—  15  o.i 

12   O.5 

22    .O 

3    2.5 

13    LI 

23   4-6 

—  10  O.I 

13   0.6 

23    .1 

4    2.1 

14   1.4 

24   5.0 

—5  0.2 

14  0.6 

24    .1 

5    1.8 

15   1.8 

25  5.3 

0  0.2 

15   0.6 

25    .2 

6    1.4 

16   2.1 

26  5.7 

+2  0.3 

1  6   0.7 

26   .3 

7    LI 

17  2.5 

27   6.0 

4-4  0.3 

17   0.7 

27   -3 

8    0.7 

18   2.8 

28  6.4 

+6  0.3 

1  8   0.8 

28   .4 

9°   0.4 

19   3-2 

29  6.7 

+8  0.4 

10   0.8 

29   -5 

872 


Barometric  Tables.       Tables  18,  a— c. 


18 a.    Reduction  of  Mercurial  Columns  to  0°.    Corrections  for  Expansion 
to  be  subtracted. 


Tempe- 
rature 

Length  in  centimetres  of  the  Mercurial  Column  measured 
by  a  Brass  Scale. 
70   71   72   73   74   75   76   77   78 

Correction 
for  glass 
scale 

cm   cm   cm   cm   cm   cm   cm   cm   cm 

0° 

0.000  0.000  0.000  0.000  O.OOO  0.000  O.OOO  O.COO  0.000 

O.OOO 

I 

Oil   Oil   012   012   012   012   OI2   012   013 

001 

2 

023  023  023  024  024  024  024  025  025 

002 

3 

034  034  035  035  036  036  037  037  038 

002 

4 

045  046  046  047  048  048  049  050  050 

OOJ 

5 

0.056  0.057  0.058  0.059  0.060  0.060  0.061  0.062  0.063 

0.004 

6 

O68   069   069   071   0/2   072   073   074   075 

005 

7 

079  080  08  I  082  083  085  086  087  088 

006 

8 

090  092  093  094  095  097  098  099  ioi 

O06 

9 

IO2   103   104   106   107   109   1  10   112   113 

007 

10 

O.II3  O.II4  O.II6  O.II8  O.II9  O.I2I  O.I22  O.I24  0.126 

O.008 

ii 

124   126   128   129   131   133   135   137   138 

OOg 

12 

*35  U7  J39  141  H3  145  H7  H9  151 

009 

13 

147  149  151  153  155  157  159  161  164 

OIO 

14 

158  160  163  165  167  169  172  174  176 

on 

15 

0.169  0.172  0.174  0.177  0.179  0.181  0.184  0.186  0.189 

0.012 

16 

181   183  186  188  191  194  196  199  201 

013 

17 

192  195  197  200  203  206  208  211  214 

013 

18 

203   206   209   212   215   2l8   221   224   227 

014 

19 

215   218   221   224   227   230   233   236   239 

015 

20 

0.226  0.229  0.232  0.236  0.239  0.242  0.245  0.248  0.252 

o.o  1  6 

21 

237   24!   244   247   251   254   258   26l   264 

017 

22 

249  252  256  259  263  266  270  273  277 

017 

23 

260   264   267   271   275   278   282   286   290 

018 

24 

271  275  279  283  287  291  294  298  302*   019 

25 

0.283  0.287  0.29!  0.295  0.299  0.303  0.307  O.3II  0.315 

0.020 

26 

294   298   302   306   3IJ   315   319   323   327 

021 

27 

305   310   314   318   323   327   331   336   340 

021 

28 

317  321  326  330  335  339  344  348  353 

022 

29 

328  333  337  342  347  35*  35^  361  365 

023 

30 

0.339  0.344  0.349  0.354  0.359  0-363  0-368  0.373  378 

024 

18 b.  Correction  for  the  Capillarity  of  Mercurial  Columns  to  be  added. 


Internal 
Diameter 
of  Tube 

o.i  cm 

0.2 

0.3 

0.4 

o.5 
0.6 
0.7 
0.8 
0.9 

I.O 

i.i 

1.2 

L3 

Height  of 
Meniscus 
unknown 

.9? 
.46 

.29 
.26 

.15 
.11 

.09 

.07 

•05 
.04 

•03 
•03 
.02 

Height  of  Meniscus  in  Centimetres 

0.04 

O.06 

0.08 

0.10 

0.12 

0.14 

0.16 

O.T8 

0.083 
.047 
.027 
.018 

O.I  22 
.065 
.041 
.028 
.O2O 
.015 

0.154 
.086 
.056 
.040 
.029 
.O2I 
.015 
.010 

.007 

.004 

0.198 
.119 
.078 

.053 

.038 

.028 
.020 
.014 

.OIO 
.007 

0.237 

•H5 
.098 
.067 
.046 

.033 
.025 
.018 
.013 
.OIO 

0.18*0 

.121 

.082 
.056 
.040 
.029 
.021 
.015 
.012 

0.143 
.097 
.065 
.046 

.033 
.024 
.018 
.013 

0.113 

.077 
.052 

.037 
.027 

.019 
.014 

18  c.    Correction  for  the  Pressure  of  Mercurial  Vapor  to  be  added. 

Temperature  o°         5°      10°      15°      20°      25°     30°      35°      40° 
Add  cm.  o.oo  i?    .001?   .002?   .002?   .002?  .002?  .003?  .003?  .004? 


Tables  18,  d— g.   .Reductions  to  0°  and  76  cm. 


873 


18,  d. 

Pres-       A 
sure       "v 


70 
71 
72 
73 
74 
75 
76 
77 


1.0857 
1.0704 
1.0556 
1.0411 
1.0270 
1.0133 

1. 0000 

.9870 


Factors  for  the  Reduction  of  the  Density  of  a  Gas  to  76  cm, 
.1    .2    .3   .4   .5    .6   .7    .8    .9   Dif, 

1.0842  1.0826  1.081 1  1.0795  1.0780  1.0765  1.0750  1.0734  1.0719 
1.0689  1.0674  I.°659  1.0644  1.0629  1.0615  i .0600  1.0585  1.0570  is 
1.0541  1.0526  1.0512  1.0497  1.0483  1.0468  1.0454  1.0440  1.0425 
1.0397  1.0383  1.0368  1.0354  T'034°  1.0326  1.0312  1.0298  1.0284 
1.0256  1.0243  1.0229  1.0215  1.0201  1.0188  1.0174  1.0160  1.0147 
1.0120  1.0106  1.0093  1.0080  1.0066  1.0053  1.0040  1.0026  1.0013 
.9987  .9973  .9961  .9948  .9935  .9922  .9909  .9896  .9883  i» 
.9857  .9845  .9832  .9819  .9806  .9794  .9781  .9769  .9756 


18,  e.    Factors  for  the  Redaction  of  the  Density  of  a  Gas  to  0°  Centigrade. 

Trtm?e~-f°°   +1°     +2°    +3°    +4°    +5°    +6°    +7°    +8°    -r9°    Dif, 
0°  i.oooo  1.0037  I-0073  i.oiio  1.0147  1.0184  1.0220  1.0257  1.0294  1.033036.7 
1.0367  1.0404  1.0440  1.0477  1.0514  1.0551  1.0587  1.0624  1.0661  1.0697   i    4 
1.0734  1.0771  1.0807  1.0844  1.0881  1.0918  1.0954  1.0991  1.1028  1.1064  9    T 
1.11011.11381.11741.12111.12481.12851.13211.13581.13951.1431  & 

I.I468l.I505I.I54II.I578l.l6l5I.l652I.l688l.I725I.I762I.I798  4 

I.I835I.I872I.I908I.I945I.I982I.20I9I.2055I.2092I.2I29I.2I65  5  is 

1.2202  1.2239  L2275  L23I2  1.2349  L2386  1.2422  1.2459  L2496  1.2532  e  22 

1.2569  1.2606  1.2642  1.2679  L27I6  1.2753  1.2789  1.2826  1.2863  1.2899  7  26 


10 
20 

30   .11011.113.174.12111.124.121.3..19.4   &  u 

40    .4.........9   4  15 

50 
60 
70 
80 
90  1.3303  L3340  1.3376  L34I3  1-3450  L3487  L3523  L3560  1.3597  1.3633  9  8, 

100°  1.3670  1.3707  1.3743  1.3780  1.3817  1.3854  1.3890  1.3927  1.3964  1.4000 


Pres- 
sure 
cm 


18,  f.    Factors  for  the  Reduction  of  the  Volume  of  a  Gas  to  76  cm. 
.0        .1        .2        .3        .4        .5        .6        .7        .8        .9       Dif. 


70   0.92II  0.9224  0.9237  O.9250  0.9263  0.9276  0.9289  O.9303  0.9316  0.9329  13.1S 


71 
72 
73 
74 
75 
76 
77 


.9342  .9355   .9368  .9382  .9395   .9408 
•9474   .9487    .9500   .9513   .9526   -9539 


.9421  .9434  .9447  .9461 
•9553  .9566  .9579  .9592 
.9605  .9618  .9632  .9645  .9658  .9671  .9684  .9697  .9711  .9724 
•9737  .9750  .9763  .9776  .9789  -9803  .9816  .9829  .9842  .9855 
.9868  .9882  .9895  .9908  .9921  .9934  .9947  .9961  .9974  .9987 
i.oooo  1.0013  1.0026  1.0039  I-0053  1.0066  1.0079  1.0092  1.0105  1.0118 
1.0132  1.0145  1.0158  1.0171  1.0184  1.0197  I.02H  1.0224  1.0237  1.0250 


1  i 

2  3 

3  4 

4  5 
b  1 

6  8 

7  9 

8  11 

9  12 


18,  g.    Factors  for  the  Rednction  of  the  Volume  of  a  Gas  to  0°  Centigrade. 


«  0°  I.OOOO 

5°  0.9820 

10°  0.9646 

15  0.9478 

20°  0.93  1  6 

25°  0.9160  30°  0.9008 

1  I  0.9963 

6  .9785 

ii  .9612 

1  6  .9445 

21   .9285 

26   .912931   .8978 

8,  2  .9927 

7  .9750 

12   .9518 

'7  «94T3 

22   .9253 

27   .9098 

32   .8949 

|  3  .9891 

8  .9715 

J3  -9545 

18  .9380 

23   .9222 

28   .9068 

33  -8920 

"  4  .9855 

9  .9680 

14  .9511 

19  .9348 

24   .9190 

29   .9038 

34  .8891 

&   36      35      34      33      32      31      29 

874  Atmospheric  Density.      Table  19   20 A. 

19.  Weight  in  grams  of  1  cubic  centimetre  of  dry  air. 


Barometric  pressure  (g  =  980.6) 

72  cm 

73cm 

74  cm 

75  cm 

76  cm 

77  cm 

Diff. 
per  cm. 

0° 

.001225 

.001242 

.001259 

.001276 

.001293 

.001310 

17 

I 

1220 

1237 

1254 

1271 

1288 

1305 

.1    2 

2 

1216 

1233 

1249 

1267 

1283 

1300 

.2    3 

3 

1212 

1228 

1245 

1262 

1279 

1296 

.3    5 

4 

1207 

1224 

1241 

1257 

1274 

1290 

.4    7 

5° 

.001203 

.001219 

.001236 

.001253 

.001270 

.001286 

.5    ~ 

6 

1198 

1215 

1232 

1248 

1265 

1282 

.6    10 

7 

II94 

I2II 

1227 

1244 

1260 

1277 

.7    13 

8 

I2O6 

1223 

1239 

1256 

1272 

.8    14 

c  9 

1186 

1202 

1219 

1235 

1251 

1268 

.0    16 

*'<>« 

.001181 

.OOlIgS 

.001214 

.001231 

.001247 

.001263 

1G 

A  II 

1177 

1194 

1210 

1226 

1243 

1259 

.1    3. 

£  12 

1189 

1206 

1222 

1238 

1255 

.2    9 

o  13 

1169 

1185 

1202 

1218 

1234 

1250 

.3    5 

4)   1  4- 

1165 

1181 

II97 

I2I4 

1230 

1246 

.4    6 

1  T-0 

.001161 

.001177 

.001193 

.001209 

.001225 

.001242 

.6    8 

2  16 

1  157 

H73 

1189 

1205 

1221 

1237 

.6    10 

2,  17 

"53 

1169 

1185 

I2OI 

1217 

1233 

.7    11 

a  is 

1149 

1165 

1181 

1197 

1213 

1229 

.3    13 

H  J9 

H45 

1161 

1177 

^93 

1209 

1224 

.9    14 

20° 

.001141 

.001157 

.001173 

.001189 

.O01204 

.001220 

15 

21  ' 

H37 

"53 

1169 

1185 

I2OO 

1216 

.1 

22 

H33 

1149 

1165 

n8i 

1196 

1212 

.2 

23 

1130 

H45 

Ii6t 

1177 

1192 

1208 

.3 

24 

1126 

1141 

"57 

"73 

1188 

1204 

'4 

25° 

.001122 

.001138 

.001153 

.001169 

.001184 

.OOI200 

.5 

26 

1118 

H34 

1149 

1165 

n  80 

1196 

.6 

27 

III4 

1130 

H45 

1161 

1176 

1192 

.7    10 

28 

IIIO 

1126 

1142 

1^57 

1172 

1188 

.8    12 

29 

1107 

1122 

1138 

1169 

1184 

.9   13 

30° 

.001103  !  .001119 

.001134 

.001149 

.001165 

.001180 

20.  Correction  for  Moisture  in  Table  19. 

PoiX   Subtl'act 

pJJJt   Subtract 

Po'irn  Subtract 

PoiS   Subtract 

—  10°   .OOO.OO1 

o°   .000,003 

--10°  .000,006 

--20°   .OOO,OIO 

—  8   .000,002 
—  6   .000,002 
—  4   .000,002 

-f-2   .000,003 
-f-4   .000,004 
-j-6   .000,004 

--I2    .000,006 
--I4    .000,007 
--16    .000,008 

--22    .000,012 
--24    .000,013 
—  26    .000,015 

—  2    .OOO,OO3 

-j-8   .000,005 

--18   .000,009 

--28    .000,016 

20  A.  Weight  in  grams  of  air  displaced  by  1  gram  of  brass  of  density  8.4. 

Density  of  Air    .00110  .00112 

.00114  .00116 

.00118 

.OOI20 

Weight  Displaced  .000131  .000133 

.000136  .000138 

.000140 

.000143 

Density  of  Air    .00120  .00122 
Weight  Displaced  .000143  .000145 

.00124 
.000148 

.00126 
.000150 

.00128   .00130 

.0001  52  j.  oooi  55 

Tables  21,22.     Reduction  of  Apparent  Weights.  875 

21.  Factors  for  the  Reduction  of  Apparent  Weighings  in  Air  with  Brass 
Weights  to  Vacno. 


Density  of  the  Air. 

Density  of  the  Air. 

.00115.  |  .00120 

.00125 

.00115 

.001  20 

.00125 

TJ  0.70 

1.00151 

LOOT  57 

1.00164 

J'   2.0 

1.00044 

1.00046 

1.00048 

£  o.75  ]  „  HO 

„  146 

ii  T52 

2-5 

»  32 

n  34 

f,  35 

.g>o.8o   „  130 

,,  136 

if  HI 

•3  3-0 

fi  25 

„   26 

ff  27 

•g  0.85  !   „  122 

ff  I27 

if  132 

>  3-5   „  19 

„   20 

W   2! 

^  0.90 

»  Ir4 

fi  "9 

„  124 

>  4-0  !  „  15 

„  16 

„  16 

8  o-95 

»  1G7 

„  IT2 

ii  U7 

8  4-5 

fi   I2 

»  I2 

»  T3 

re  1.0 

I.OOIOI 

I.OOI06 

1.  00  1  ip 

§  5.0 

1.00009 

1.  000  TO 

I.OC-OIO 

1  T-r 

1.00091 

1.00095 

1.0009*9 

I  6.0 

1.00005 

1.00006 

1.00006 

•§  1.2 

„   82 

„  86 

»  89 

a  7.0 

ff  3 

n  3 

»  3 

<"  1-3 

if  75 

f,  78 

„  81 

M  8.0 

ii  i 

»   ! 

if   r 

^  1.4 

„  68 

ff  71 

»  74 

.S  9-0 

0.99999 

0.99999 

0.99999 

£  i-5 

1.00063 

1.00066 

1.00068 

£  I0 

0.99998 

0.99998 

0.99998 

o  1.6 

„  58 

„  61 

»  63 

0  12 

»  6 

n  6 

n  5 

£•  1-7 

»  54 

„  56 

ff  59 

>PH 

ff  5 

n  4 

„  4 

5  1.8 

»  50 

»  52 

»  55 

'co  l6 

ff  3 

ff  3 

n  3 

5  1.9 

ff  47 

i)  49 

»  51 

<D  1  8 

ff  3 

if   2 

if   2 

Q  2.0 

1.00044 

1.00046  1.00048 

Q  20 

0.99992 

0.99992 

0.9999! 

Apparent  Specific  Volume  of  Water. 

22.  Space  in  cubic  centimetres  occupied  by  a  quantity  of  Water  weighing 

apparently  1  grain  when  counterpoised  in  Air  with  Brass  Weights  of  the 

Density  8.4. 


D  ensity  of  the  Air 

.001  TO 

.00115 

.00120 

.00125 

.00130 

0° 

1.00109 

1.00113 

1.00117 

I.OOI22 

1.00126 

I 

ff  103 

ff  I07 

if  II2 

,,  "6 

ff  J2I 

2 

1.00099 

ff  103 

ii  Io8 

ff  "2 

„  1  16 

3 

ff  97 

ff  I01 

if  i°6 

ff  IJ0 

ff  "4 

•  4 

»  96 

ff  ioo 

ff  I05 

ii  I09 

fi  IH 

-o 
D 

1.00097 

I.OOIOI 

1.00106 

I.OOIIO 

1.00114 

6 

»  99 

ff  103 

»  1  08 

ff  II2 

ff  IT7 

c   7 

1.00103 

,,  107 

„  in 

ff  U6 

ff  "O 

v   8 

»  108 

,,^12 

„  "6 

„  121 

ff  I25 

*   9 

ff  iH 

ii  »8 

,,  123 

ff  I27 

ff  I3i 

£   10° 

I.OOI22 

1.00126 

1.00131 

1.00135 

1.00139 

«!    TI 

fi  T3t 

if  135 

If  HO 

ff  H4 

ff  H8 

.s   12 

ff  HI 

ff  H6 

ff  X50 

ff  T55 

ff  159 

13 

»  153 

,,  158 

„  162 

ff  I66 

ff  171 

*S  H 

if  !66 

ff  X7i 

if  J75 

ff  179 

,,  184 

«  15° 

1.  00  1  8O 

1.00185 

1.00189 

1.00194 

1.00198 

«-  16 

ff  T96 

„  200 

ff  205 

„  209 

ff  214 

2  17 

„  212 

fl  217 

ff  221 

fi  225 

ff  230 

«  18 

j^l 

ff  231 

ff  235 

if  239 

ff  244 

„  248 

«   19 

ff  250 

If  254 

ll  258 

,,263 

ff  267 

p   200 

1.00270 

I.O0275 

1.00279 

1.00283 

1.00288 

S   21 

ff  291 

ff  295 

ff  3CO 

ff  304 

ff  309 

H   22 

if  313 

,,  318 

ff  322 

ff  326 

ff  33i 

23 

ff  336 

ff  340 

ff  344 

ff  349 

ff  353 

24 

fl  360 

ff  364 

n  368 

ii  373 

if  377 

25° 

1.00384 

1.00389 

1.00393 

1.00398 

1.00402 

26 

ff  410 

If  4H 

if  4'9 

»  423 

,,428 

27 

ff  437 

ff  441 

ii  445 

fi  450 

f,  454 

28 

ff  464 

ll  468 

ff  473 

ff  477 

,,482 

29 

„  492 

ff  497 

ii  50i 

fi  5°5 

w  5io 

30°   1.00521 

1.00525 

1.00530 

1.00534 

1.00538 

876 

23. 


Specific  Volumes.     Tables  23—  23  B. 


Space  in  en  cm  occupied  by  a  quantity  of  Water  weighing  1  gram 
in  Vacuo. 


O°  1  .0001  2  Dif. 

25°  1.00287  Dif. 

50°  i.  01  1  94  Dif. 

750  1.02565  Dif 

I  1.00006  —  * 

26  1.00313  26 

51  I.OI242  48 

76  1.02629  w 

2   1.00002  —  4 

27  1.00339  26 

52  1.01291  49 

77  1.02693  M 

3  i.  ooooo  —  2 

28  1.00367  28 

53  1.01340  49 

78  1.02757  64 

4  °-99999  -1 

29  1.00395  28 

54  1.01389  « 

79  1.02821  6* 

5°  i.  ooooo  +1 

30°  1.00424  29 

55°  1.01438  49 

80°  1.02886  65 

6  1.00002  a 

31  1.00454  3° 

56  1.01487  49 

8  1  1.02931  65 

7  1.00006  * 

32  1.00485  31 

57  1.01536  49 

82  1.03017  66 

8  i.oooii 

33  1.00517  32 

58  1.01586  50 

83  1.03084  67 

9  1.00017  6 

34  i  00550  33 

39  1.01637  5l 

84  I.03I52  68 

10°  1.00025  8 

35°  1.00585  35 

60°  1.01690  53 

85°  1.03220  & 

ii  1.00034  9 

36  1.00620  35 

61  1.01743  53 

86  1.03288  68 

12   1.00044   1 

37  1.00656  36 

62  1.01797  w 

87  1.03357  69 

13   1.00056   12 

38  1.00693  37 

63  1.01851  54 

88  1.03426  69 

14   I.OOObg   13 

39  1.00731  » 

64  1.01907  56 

89  1.03496  70 

15°  1.00083   '* 

40°  1.00769  38 

65°  1.01963  56 

90°  1.03566  70 

1  6  1.00099  3 

41  1.00808  39 

66  1.02020  57 

91  1.03637  71 

17  1.00115 

42  1.00848  40 

67  1.02077  57 

92  1.03709  72 

18  1.00133  : 

43  1.00888  *o 

68  I.02I36  59 

93  1.03781  72 

19  1.00152  19 

44  1.00928  40 

69  I  02195  59 

94  1.03855  74 

20°  I.OOI73  21 

45°  1.00970  « 

70°  1.02255  6° 

95°  1.03930  75 

21   I.OOIQ4  ' 

46  1.01013 

71  1.02315  60 

96  I.O4O05  75 

22   I.002I6  22 

47  1.01056  43 

72  1.02377  62 

97  1.04081  76 

23   1.00238  28 

48  I.OIIOI  *5 

73  1.02439  62 

98  1.04157  76 

24   1.00262  24 

49  1.01147  « 

74  1.02502  63 

99  1.04234  77 

25°  1.00287  25 

50°  1.01194  *7 

75°  1.02565  63 

100°  1.04311  77 

A.    Space  in  cu.  cm.  occupied  by  1  gram  of  Mercury. 


o°  0.073,551 

10°  0.073,684 

20°  0.073,8l6 

Dif. 

I  .073,564 

ii   .073,697 

21    .073,830 

13  14 

2    .073,578 

12    .073,710 

22    .073,843 

.iii 

3   -073,591 

13    -073,723 

23    .073,856 

.233 

4   .073,604 

H    .073,737 

24    .073,870 

•3  4  £ 

5°  0.073,617 

15°  0.073,750 

25°  0.073,883 

.4  5  6 

6   .073,631 

1  6   .073,763 

26    .073,896 

•5  7  7 

7   .073,644 

17  .073,776 

27    .073,910 

.688 

8   .073,657 

18   .073,790 

28    .073,923 

•7  9  IO 

9   .073,670 

19   .073,803 

29    .073,936 

.8  10  ii 

10°  0.073,684 

20°  0.073,8l6 

30°  0.073,950 

.9  12  13 

23,  B.    Space  in  cu.  cm.  occupied  by  a  quantity  of  Mercury  weighing 

apparently  1  gram  when  balanced  by  Brass  Weights  of  Density  8.4  in 

Air  of  Density  .0012. 


o°  0.073,547 

10°   0.073,680 

20°   0.073,812 

Dif. 

I     .073,560 

II     .073,693 

21         .073,826 

13  14 

2         .073,574 

12          .073,706 

22         .073,839 

.iii 

3      -073,587 

!3       •073,7I9 

23         .073,852 

.2     3     3 

4       .073,600 

IA       -073733 

24         .073,866 

•344 

5°  0.073,613 

15°  0.073,746 

25°    0.073,879 

4     5     6 

6        .073,627 

16       .073,759 

26         .073,892 

.<;    7    ? 

7       .073,640 

17       .073,772 

2/          .073,906 

.6     8     8 

8       .073,653 

1  8       .073,786 

28         .073,919 

.7      9    10 

9       .073,666 

'9       .073.799 

2Q         .073,932 

.8    10    ii 

10°  0.073,680 

20°   0.073,812 

30°    0.073,946 

•9    12    13 

Tables  24—26.      Standard  Densities. 


877 


Density  of  Water,  Mercury  and  Glycerine. 

24.  Density  of  Mercury  at  different  temperatures. 


0° 

13.596 

90° 

13.377 

1  80° 

I3.I62 

270° 

12.948 

10° 

13.572 

TOO0 

13.353 

IgO0 

13.138 

280° 

12.924 

20° 

13.547 

IIO° 

13.329 

200° 

I3.H4 

290° 

12.900 

30° 

13.523 

120° 

13.305 

210° 

13.091 

300° 

12.876 

40° 

13.498 

I300 

H.28I 

220° 

13.067 

310° 

12.853 

50° 

13.474 

140° 

13.257 

230° 

13.043 

320° 

12.829 

60° 

13.450 

I500 

13.233 

240° 

13.019 

330° 

12.805 

70° 

13.426 

1  60° 

13.210 

2500 

12.995 

340° 

12.781 

80° 

13.401 

I700  • 

13.186 

260° 

12.972 

350° 

12.757 

25.  Density  of  Water  at  different  temperatures. 


o°  0.99988 

25°  0.99714 

50°  0.98819 

75°  0.97497 

I       94 

26   .99687 

51     772 

76     437 

2       98 

27      61 

52     725 

77     3/6 

3   i.  ooooo 

28      34 

53     677 

78     315 

4      01 

29      06 

54     629 

79     254 

5°  i.  ooooo 

30°  0.99578 

&5°  0.98582 

80°  0.97193 

6   0.99998 

3i    .  548 

56     534 

81     131 

7      94 

32     518 

57     486 

82     069 

8      89 

33     486 

58     437 

83     006 

9      83 

34     453 

59     388 

84   .96942 

10°  0.99975 

35°  0.99419 

60°  0.98338 

85°  0.96878 

ii      .66 

36     384 

61     286 

86     814 

12        56 

37     348 

62     234 

87     750 

13       44 

38     3ii 

63     181 

88     686 

H       31 

39     274 

64     127 

89     621 

15°  0.99916 

40°  0.99236 

65°  0.98073 

90°  0.96554 

16       01 

41     198 

66     01  8 

91     488 

17    .99885 

42     158 

67   .97963 

92     421 

18      67 

43     "8 

68     907 

93     354 

19      48 

44     078 

69     850 

94     286 

20°   0.99828 

45°  0.99037 

70°  0,97793 

95°  0.96216 

21         07 

46   .98996 

7i     735 

96     146 

22     .99785 

47     954 

72     676 

97     076 

23         62 

48     910 

73     617 

98     005 

24      39 

49     865 

74     557 

99   -95934 

25°  0.99714 

50°  0.98819 

75°  0.97497 

100°  0.95863 

26.  Density  of  Commercial  Glycerine  <o»— 30°). 


o°  1.269 

5°  1.266 

10°  1.263 

I50  1.260 

200   .257 

25°  .2^3 

1°  1.268 

6°  1.265 

11°  1.262 

16°  1.259 

21°   .256 

26°  .253 

2°  1.268 

7°  1-265 

12°  1.262 

17°  1.258 

22°   .255 

27°  .252 

3«>  1.267 

8°  1.264 

13°  I.26I 

1  8°  1.258 

23°   .255 

28°  .252 

4°  1.267 

9°  1.263 

14°  1.260 

19°  1.257 

24°   .254 

29°  .251 

5°  1.266 

10°  1.263 

15°  1.260 

20°  1.257 

25°   .253 

30°  .251 

878 


Density  of  Alcohol. 


Table  27. 


w't 

VOL.  I5°|  15°  |  16° 

17° 

18° 

19° 

20° 

21° 

22° 

0 

o.oo 

.9992 

.9990 

.9988 

.9987 

•9985 

•9983 

.9981 

•9979 

I 

1.26 

.9971 

.9969 

.9967 

.9966 

.9964 

.9962 

.9960 

•9958 

2 

2.51 

•9953 

•9951 

•9949 

•9947 

•9945 

•9943 

•9942 

•9940 

3 

3-75 

•9936 

•9934 

•9932 

•9930 

.9928 

.9926 

•9924 

.9922 

4 

5.00 

.9920 

.9918 

-9916 

.9914 

.9912 

.9909 

.9907 

•9905 

6.24 

•99°3 

.9901 

•9899 

.9897 

•9895 

.9892 

.9890 

.9888 

5 

7-47 

.9887 

.9885 

•9883 

.9880 

.9878 

.9876 

•9874 

.9872 

7 

8.70 

.9871 

.9869 

.9866 

.9864 

.9861 

•9859 

•9857 

•9855 

8 

9-93 

.9856 

•9854 

.9851 

.9849 

.9846 

.9844 

.9842 

•9839 

9 

ii.  16 

.9842 

-9839 

•9837 

•9834 

.9832 

.9829 

.9827 

.9824 

10 

12.38 

.9828 

.9825 

•9823 

.9820 

.9817 

•9815 

.9813 

.9810 

ii 

f9 

.9814 

.9811 

-9809 

.9806 

.9803 

.9800 

.9798 

•9795 

12 

.  i 

.9801 

.9798 

•9795 

•9793 

•979° 

•9787 

.9784 

.9781 

J3 

16.03 

•9789 

.9786 

•9783 

.9780 

•9777 

•9774 

.9772 

.9769 

H 

17.24 

•9777 

•9774 

.9771 

.9768 

.9765 

.9762 

•9759 

•9756 

15 

•9765 

.9762 

•9759 

•9755 

•9752 

•9749 

.9746 

•9743 

16 

19.65 

•9753 

•9750 

.9746 

•9743 

.9740 

.9736 

•9733 

.9730 

17 

20.85 

.9741 

•9738 

•9734 

•973i 

•9727 

.9724 

.9721 

.9717 

18 

22.05 

•9729 

.9725 

.9722 

.9718 

•9715 

.9711 

.9708 

-9704 

IQ 

23-25 

.9718 

.9714 

.9711 

•9707 

•9703 

.9699 

.9696 

.9692 

2O 

24-45 

.9707 

•9703 

.9699 

.9691 

.9687 

.9683 

.9679 

21 

25.64 

.9691 

.9687 

.9683 

.9679 

.9674 

.9670 

.9666 

22 

26.83 

.9683 

.9679 

.9674 

.9670 

.9666 

.9661 

•9657 

•9653 

23 

28.01 

.9671 

.9666 

.9662 

•9657 

•9653 

.9648 

.9644 

•9639 

24 

29.19 

•9659 

•9654 

.9650 

.9645 

.9640 

.9635 

.9631 

.9626 

25 

30.37 

.9647 

.9642 

•9637 

.9632. 

.9627 

.9621 

.9617 

.9612 

26 

3r.54 

.9633 

.9628 

.9623 

.9618 

.9613 

.9607 

.9602 

•9597 

27 

.9619 

.9614 

.9608 

.9603 

•9598 

•9592 

.9587 

.9582 

28 

33*86 

.9604 

•9599 

•9593 

-9588 

•9583 

•9577 

•9571 

.9566 

29 

35.02 

.9589 

.9583 

•9578 

•9572 

.9567 

.9561 

•9555 

•9549 

30 

36.17 

•9573 

.9567 

.9561 

•9556 

•9550 

•9544 

.9538 

•9532 

31 

37.30 

•9556 

•9550 

-9544 

•9538 

•9532 

.9526 

.9520 

•95H 

32 

38.44 

•9539 

•9533 

•9527 

.9521 

.9515 

•9508 

.9502 

.9496 

33 

39-57 

.9522 

.9516 

•9509 

•9503 

•9497 

.9490 

.9484 

.9478 

34 

40.69 

.9504 

.9498 

.9491 

.9485 

•9479 

.9472 

.9466 

•9459 

35 

41.81 

.9486 

•9479 

•9m 

.9466 

.9460 

•9453 

•9447 

.9440 

36 

42.92 

.9467 

.9460 

•9454 

-9447 

.9440 

•9433 

.9427 

.9420 

37 

44.02 

.9448 

.9441 

-9434 

.9428 

.9421 

.9414 

.9407 

.9400 

38 

45.12 

.9429 

.9422 

.9415 

.9408 

.9401 

•9394 

.9388 

.9381 

39 

46.21 

.9410 

.9403 

•9396 

•9389 

•9382 

•9375 

-9368 

.9361 

40 

47.30 

•9390 

.9383 

•9376 

•9369 

.9362 

•9354 

•9347 

•9340 

48.38 

•9370 

•9363 

•9356 

•9348  ' 

•9341 

•9334 

•9327 

.9320 

42 

49-45 

•9349 

•9342 

-9334 

•9327 

.9320 

.9312 

•9305 

.9298 

43 

50.51 

.9328 

.9321 

•93J3 

.9306 

.9298 

.9291 

.9284 

.9276 

44 

51.57 

«93°7 

.9299 

.9292 

.9284 

•9277 

.9269 

.9262 

.9254 

45 

52.62 

.9286 

.9278 

.9271 

.9263 

.9256 

.9248 

.9240 

•9233 

46 

53.67 

.9265 

.9257 

.9250 

.9242 

•9234 

.9226 

.9219 

.9211 

47 

54-7i 

.9244 

.9236 

.9229 

.9221 

.9213 

.9205 

.9198 

.9190 

48 

55-75 

•9223 

.9215 

.9207 

.9200 

.9192 

.9184 

.9176 

.9168 

49 

56.78 

.9201 

•9193 

.9185 

.9178 

.9170 

.9162 

•9*54 

.9146 

50 

57.80 

•9*79 

.9171 

.9163 

•9X55 

.9147 

•9*39 

.9132 

.9124 

Table  27. 


Density  of  Alcohol. 


879 


w't 

VOL.  15° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

50 

57.80 

.9179 

.9171 

.9163 

•9155 

.9147 

-9J39 

.9132 

.9124 

51 

58.81 

•9157 

.9149 

.9141 

-9J33 

.9125 

.9117 

.9110 

•9IO2 

S2 

59-82 

•9135 

.9127 

.9119 

.9111 

.9103 

-9095 

.9087 

.9079 

53 

60.82 

•9JI3 

.9105 

.9097 

.9089 

.9081 

•9073 

.9065 

•9057 

54 

61.82 

.9091 

.9083 

•9075 

.9067 

•9°59 

.9050 

.9042 

•9°34 

55 

62.81 

.9069 

.9061 

•9053 

•9°45 

•9°37 

.9028 

.9020 

.9012 

56 

63-79 

.9046 

.9038 

.9030 

.9022 

.9013 

.9005 

•8997 

.8989 

57 

64.77 

.9023 

.9015 

.9007 

.8998 

.8990 

.8982 

•8974 

.8966 

58 

65-74 

.9000 

.8992 

.8984 

.8975 

.8967 

.8959 

.8951 

•8943 

59 

66.70 

.8977 

.8969 

.8961 

.8952 

.8944 

.8936 

.8928 

.8920 

60 

67.65 

•8954 

.89^6 

-8938 

.8929 

.8921 

.8913 

•8905 

.8897 

61 

68.60 

.8931 

.8923 

.8914 

.8906 

.8898 

.8890 

.8882 

.8873 

62 

69-55 

.8908 

.8900 

.8891 

.8883 

.8875 

.8867 

•8859 

.8850 

63 

70.49 

.8885 

.8877 

.8868 

.8860 

.8852 

.8844 

.8836 

.8827 

64 

71.42 

.8862 

•8854 

•8845 

.8837 

.8829 

.8821 

.8813 

.8804 

65 

72-34 

.8838 

.8830 

.8821 

•8813 

.8805 

.8797 

.8789 

.8780 

66 

73.26 

.8815 

.8807 

.8798 

.8790 

.8782 

•8773 

.8765 

.8756 

6? 

74.18 

.8792 

.8784 

•8775 

.8767 

•8759 

.8750 

.8742 

•8733 

68 

75.08 

.8768 

.8760 

•8751 

-8743 

•8735 

.8726 

.8718 

.8709 

69 

75-98 

.8744 

.8736 

.8727 

.8719 

.8711 

.8702 

.8694 

.8685 

70 

76.88 

.8721 

•8713 

.8704 

.8696 

.8688 

.8679 

.867I 

.8662 

7i 

77-77 

.8698 

.8689 

.8681 

.8672 

.8664 

-8655 

.8647 

.8638 

72 

78.65 

.8674 

.8665 

.8657 

.8648 

.8640 

.8631 

•8623 

.8614 

73 

79-  5  J 

.8649 

.8640 

.8632 

.8623 

.8615 

.8606 

.8598 

-8589 

74 

80.37 

.8625 

.8616 

.8608 

•8599 

.8591 

.8582 

•8574 

-8565 

75 

81.23 

.8601 

.8592 

.8584 

•8575 

.8567 

.8558 

•8550 

.8541 

76 

82.08 

.8576 

.8567 

.8559 

•8550 

.8542 

•8533 

.8525 

.8516 

77 

82.92 

-8552 

•8543 

•8535 

.8526 

.8518 

.8509 

.8501 

.8492 

78 

83-76 

.8528 

.8519 

.8511 

.8502 

.8494 

.8485 

.8476 

.8468 

79 

84-59 

•8503 

.8494 

.8486 

.8477 

.8469 

.8460 

.8451 

.8443 

80 

85-41 

.8478 

.8469 

.8461 

.8452 

•8444 

•8435 

.8426 

.8418 

81 

86.22 

•8453 

.8444 

.8436 

.8427 

.8419 

.8410 

.8401 

-8393 

82 

87.03 

.8428 

.8419 

.8411 

.8402 

'8394 

•8385 

.8376 

.8368 

83 

87.84 

.8404 

.8395 

.8387 

.8378 

.8370 

.8361 

•8352 

•8344 

84 

88.63 

•8379 

.8370 

.8362 

-8353 

•8345 

•8336 

.8327 

.8319 

85 

89.42 

.8354 

.8345 

-8337 

.8328 

.8320 

.8311 

.8302 

.8294 

86 

90.20 

.8329 

.8320 

.8312 

•8303 

.8295 

.8286 

.8277 

.8269 

87 

90.97 

•8303 

.8294 

.8286 

.8277 

.8269 

.8260 

.8251 

•8243 

88 

91.72 

.8277 

.8268 

.8260 

.8251 

.8243 

•8234 

.8225 

.8217 

89 
90 

92.47 
93.22 

.8251 
.8225 

.8242 
.8216 

.8234 
.8208 

•8225 
.8199 

.8217 
.8190 

.8208 
.8181 

.8l99 
•8173 

.8191 
.8164 

91 

93-96 

.8199 

.8190 

.8182 

•8i73 

.8164 

•8i55 

.8147 

.8138 

92 

94.68 

.8172 

.8163 

-8155 

.8146 

•8i37 

.8128 

.8120 

.8111 

93 

95-39 

.8145 

.8136 

.8128 

.8119 

.8110 

.8101 

.8093 

.8084 

94 

96.09 

.8118 

.8109 

.8101 

.8092 

.8083 

.8074 

.8066 

.8057 

95 

96.78 

.8090 

.8081 

.8073 

.8064 

.8055 

.8046 

.8038 

.8029 

96 

97-45 

.8061 

.8052 

.8044 

•8035 

.8026 

.8017 

.8009 

.8000 

97 

98.11 

.8032 

.8023 

.8015 

.8006 

•7997 

.7988 

.7980 

•797  1 

98 

98.75 

.8002 

•7993 

•7985 

.7976 

.7967 

•7958 

•7950 

.7941 

99 

99-38 

•7972 

-7963 

•7955 

•7946 

•7937 

.7928 

.7920 

.7911 

100 

IOO.OO 

.7941 

•7932 

•7924 

.7915 

.7906 

.7897 

.7889 

.7880 

380              Density  of  Solutions  at  15°. 

Table  28. 

*                         V.                            ' 

.'H 

-o 

o 

£ 

"o 

*0 

ftt 

rt) 

a 

"3 

6 

<0 

< 

*§.   n 

i  „ 

<o 

11 

-A 

20^ 

S-S 

Id 

O 

Uj? 

£" 

«DH 

<<s 

•cO 

.fez 
££ 

a* 

fii 

IS 

gw 
<.s 

II 

^"o  rt 

Ec/te 

Us 

fe 

Su 

m 

0 

0.999  0.999 

0.999  °-999 

0.999 

0.719 

0.999 

0.999 

0.999 

0.999 

0.999 

2 

1.002 

1.010 

I.OIO 

I.OIO 

1.008 

.721 

.993 

1.  02 

1.  02 

1.004 

1.007 

4 

1.005 

1.022 

1.  02  1 

1.024 

1.017 

.723 

.989 

1.04 

1.03 

1.009 

1.015 

6 

1.008 

1.035 

1.032 

1.039 

1.026 

.724 

•985 

T.O6 

1.05 

1.014 

1.023 

8 

1.  01  1 

1.047 

1.044 

1.053 

1.036 

.726 

.982 

1.09 

1.07 

1.019 

1.031 

10 

1.014 

1.059 

1.056 

1.068 

1.045 

0.728 

0.980 

i.  n 

1.09 

1.024 

1.039 

12 

1.017 

1.068 

1.084 

1.055 

.729 

.978 

1.^3 

I.  II 

1.030 

1.047 

14 

I.O20 

1.083 

i.  080 

1.099 

1.065 

.731 

.976 

1.16 

1.  12 

1.035 

1.056 

16 

1.023 

1.096 

1.093 

1.114 

1.075 

.733 

•974 

1.18 

1.14 

1.040 

1.065 

18 

1.026 

I.I08 

1.106 

1.129 

1.085 

•734 

•972 

1.  20 

1.16 

1.045 

1.073 

20 

1.028 

1.  121 

1.119 

1.144 

1.095 

0.736 

0.970 

1.22 

1.18 

1.050 

1.082 

22 

I.03I 

I.I34 

.132 

1.  160 

I.IOO 

.738 

.968 

1.24 

i.  20 

1.055 

1.091 

24 

1.034 

I.I47 

.146 

I.I75 

I.n6 

•739 

.965 

1.27 

1.22 

i.  06  1 

1.  100 

26 
28 

1.036 
1.039 

1.160 

.159 
.174 

1.191 
1.207 

1.127 
1.138 

.741 
•743 

•963 
.961 

1.29 
I.3I 

a 

1.066 
1.071 

i.  no 
1.119 

30 
32 

I.04I 
1.044 

1.186 
1.199 

.188 
.204 

1.224 
1.240 

1.149 

1.100 

0-745 
.746 

0-959 
•957 

1.33 

1-35 

1.29 

1.076 
1.081 

1.129 
1.138 

34 

1.046 

1.213 

.218 

1.257 

1.171 

.748 

•955 

i.37 

1.33 

1.086 

1.148 

36 

1.048 

1.226 

.233 

1.274 

1.182 

.750 

•953 

1.39 

1.36 

1.092 

1.158 

38 

1.050 

1.239 

.248 

1.290 

1.193 

•751 

.950 

1.41 

1.39 

1.097 

1.168 

40 

1.052 

1.252 

1.264 

1.306 

1.205 

0.753 

0-947 

1.44 

1.41 

1.  102 

1.178 

42 

1.054 

1.265 

1.280 

1.323 

1.217 

•754 

•945 

1.46 

1.43 

I.I07 

1.189 

44 

1.056 

1.278 

1.297 

1.340 

1.229 

•756 

•943 

1.48 

1.45 

1.  112 

1.199 

46 

1.058 

1.292 

I.3I3 

1.361 

1.240 

.757 

.940 

1.50 

1.48 

I.II7 

I.2IO 

48 

1.  060 

1.305 

1.380 

1.253 

•759 

.938 

1.52 

I«5I 

I.I22 

I.22I 

50 

1.062 

1.318 

1.348 

1.399 

1.26 

0.760  0.935 

1.54 

1-53 

I.I27 

1.232 

52 

1.063 

1.330 

1365 

1.418 

1.28 

.761 

.932 

1.56 

1.56 

I.I32 

1.243 

54 

1.065 

1.342 

1.383 

1.438 

1.29 

.763 

.929 

1.58 

1.58 

I.I37 

1.254 

56 

1.066 

1.353 

1.401 

1-459 

1.30 

.764 

.926 

i.  60 

1.61 

I.I43 

1.266 

58 

1.067 

1.364 

1.420 

1.480 

1.32 

.765 

.923 

1.62 

1.64 

1.148 

1.277 

60 

1.069 

1-375 

1.439 

1.502 

0.766 

0.919 

1.64 

1.66 

I.I53 

1.289 

62 

1.070 

1.386 

L525 

.767 

.915 

1.66 

1.69 

I.I58 

1.301 

64 

I.07I 

1.396 

1.540 

.769 

.911 

1.68 

1.72 

1.163 

I.3I3 

66 

1.072 

1.405 

1.568 

.770 

.905 

1.70 

1.168 

1.325 

68 

1.073 

1.414 

I.59I 

.771 

.900 

1-73 

1.77 

I.I73 

1-337 

70 

1.073 

1.423 

1.615 

0.773 

0.896 

1-75 

1.79 

1.178 

1.350 

72 

1.074 

I«43* 

1.638 

•774 

.890 

1.183 

1.363 

74 

1.074 

1.438 

1.662 

•775 

.885 

1.188 

T-375 

76 

1.075 

1-445 

1.686 

-777 

.880 

1.^93 

78 

L075 

1.453 

1.710 

.778 

.873 

1.198 

80 

L075 

1.460 

1-734 

0.779 

0.868 

1.8? 

2.0? 

1.203 

82 

I-°75 

1.467 

L758 

.781 

.862 

1.209 

84 

1.074 

1.474 

1.774 

.782 

.857 

1.214 

86 

1.074 

1.481 

1.791 

.784 

.851 

1.220 

88 

1.073 

1.488 

1.807 

.785 

.846 

1.225 

90 

1.071 

M95 

1.819 

0.786 

0.840 

1.9? 

2.1? 

I.23I 

92 

1.070 

1.502 

1.829 

.788 

.835 

1-237 

94 

1.069 

1.509 

1.836 

.789 

.829 

1.242 

96 

1.064 

1.516 

1.840 

.791 

.823 

1.248 

98 

i.  060 

L523 

1.841 

•793 

.817 

1.254 

100 

1-055 

1.530 

1.839 

0.794 

0.810 

2.0? 

2.2? 

1.260 

Table  28.      Density  of  Solutions  at  15' 


881 


0 

' 

O   Oj 

O 

O 

•-50 

«*H 

IH 

e          wO       a 

i- 

H 

*5 

«  « 

l£8 

•8s 

*C  3-? 

,2'oU 

4) 

rs 

|«j§ 
°%m 

i|| 

O 

Ili 

|oq  ||q  |oq 

£ 

ffi-cX 

S$y£ 

u°« 

533 

USN 

sl' 

§UCJ 

§c«^ 

wcS^  S«?  IN? 

o 

0.999 

0.999 

0.999 

0.999 

0.999 

0.999 

0.999 

0.999 

0.999  0.999  0.999 

2 

1.009 

.990 

1.017 

1.016 

1.019 

I.OIO 

I.OI  I 

I.OI2 

I.OIO   1.009   I.OI2 

4 

1.019 

.982 

1.036 

1.033 

1.036 

I.02O 

1.024 

1.025 

1.020  1.018  1.023 

6 

1.029 

.974 

L054 

1.051 

1.052 

I.03I 

1.038 

1.039 

1.031  1.028  1.034 

8 

1.039 

.966 

1.073 

1.068 

1.071 

1.04! 

1.052 

1.053 

1.042  1.038  1.046 

10 

1.049 

0.958 

1.092 

1.086 

I.OgO 

1.052 

1.065 

1.067 

1.053  1.048  1.058 

12 

1.059 

.951 

i.  in 

1.105 

1.109 

1.063 

1.077 

1.082 

1.064  1.058  1.072 

14 

1.069 

.944 

1.131 

1.123 

I.I27 

L074 

1.091 

1.096 

1.076  1.068  1.084 

16 

1.079 

.937 

1.151 

1.142 

I.I45 

1.085 

1.105 

I.IIO 

1.087 

.078 

.096 

18 

1.089 

.930 

1.171 

1.162 

1.164 

L097 

1.119 

1.125 

1.099 

.088 

.109 

20 

1.  1  00 

0.924 

1.192 

1.181 

I.I85 

I.I08 

1.134 

1.141 

I.III 

.099 

.123 

22 

i.  no 

.918 

1.213 

1.202 

1.206 

1.  120 

1.151 

1.157 

1.124 

,I09 

.136 

24 

1.  120 

.912 

1.234 

1.222 

1.227 

I.I31 

1.171 

1.136 

.I2O 

•T49 

26 

1.130 

.907 

1.256 

1.244 

1.248 

I.I43 

1.191 

1.189 

1.148 

.131 

.163 

28 

1.140 

.902 

1.278 

1.265 

1.269 

I.I55 

1.  211 

1.206 

1.160 

.142 

.178 

30 

1.150 

0.897 

1.300 

1.287 

1.290 

1.167 

I.23I 

1.223 

1.173 

.153 

.193 

32 

1.160 

.892 

1.323 

I.3IO 

1.315 

1.179 

1.250 

1.240 

1.186 

.164 

.208 

34 

1.170 

.887 

1.346 

1.332 

1.339 

1.19! 

1.270 

1.258 

1.199 

•175 

.223 

36 

1.180 

.883 

L370 

1.355 

1.365 

I.2O4 

1.290 

1.276 

I.2I2 

.186 

.239 

38 

1.190 

1.394 

L379 

1.391 

1.216 

I.3IOI.295 

1.225 

.198 

.254 

40 

1.200 

1.418 

1.402 

1.419 

1.229 

L33I 

1.315 

1.238 

,2IO 

.270 

42 

1.442 

1.445 

1.242 

1.352 

1.335 

.222 

.287 

44 

1.467 

1.472 

L255 

L374 

1.355 

•234 

.303 

46 

1.492 

1.499 

1.268 

1-397 

1-375 

.246 

.319 

48 

1.518 

1.532 

1.281 

1.420 

1.396 

•259 

.336 

50 

1-543 

1.565 

1.294 

1-443 

1.417 

.271 

.352 

52 

1.570 

1-599 

1.468 

.284 

.369 

54 

1.633 

1.493 

.297 

.387 

56 

1.668 

L5I9 

1.405 

58 

1.703 

1.424 

60 

1-739 

d     1-444 

lid 

«c 

<*•  e 
°  § 

*oS 

*o 

°S~ 

JL 

*s  S 

1     "**                               (/> 

c 
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9J.J, 

S-2/J? 

||8 

4ia^ 

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°EZ 

i'L 

I-SG 

3J 

'ii 

B2o 
o  o  „ 

|£cj 

3 

^'v5  w 
£  ^O 

'^JSO  ^^o  %'jz 

0° 

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rt*.—  ^ 

se  » 

3  «  OD 

3*"^  rt 

ss'3 

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*5  ^E     ^5*^  2     *~  CO 

& 

<C-ic? 

U  o'Z 

u<n 

uSS 

UcnZ 

u£* 

S  °^' 

Zf2^ 

w  a"?  en'0  *  c75<a) 

0 

0.999 

0.999 

0.999 

0.999 

0-999 

0.999 

0-999 

0.999 

0.999  0-999  !'999 

2 

1.013 

I.02I 

1.005 

1.016 

1.014 

I.OI2 

I.OI 

I.OI  I 

i.oi  2  1.007  I>004 

4 

1.027 

I.O42 

I.OI2 

1.033 

1.028 

1.025 

1.03 

1.023 

1.024  1.015  1*009 

6 

1.042 

1.063 

I.OI8 

1.050 

1.043 

1.038 

1.04 

1.035 

1.037  1.023  1*015 

8 

1.057 

1.084 

1.024 

1.067 

1.058 

I.O52 

1.054-1.048 

1.051    I.O3I    I«02I 

10 

1.072 

1.  1  06 

1.030 

1.085 

1.072 

1.065 

1.07 

1.  06  1 

1.064  1.039  1.027 

12 

1.088 

I.I28 

1.036 

1.103 

1.088 

1.079 

i.  08 

1.074 

1.078  1.047  1.033 

H 

1.105 

I.I5O 

1.042 

1.  121 

1.103 

L093 

I.IO 

1.088 

1.091  1.055  1.040 

16 

1.  121 

1.175 

1.047 

I.I40 

1.118 

1.107 

.102 

1.105  1.063  1.047 

18 

I.I32 

1.200 

1.053 

I.I58 

I.I34 

1.  121 

.116 

1.  120   1.072   I.OfJ4 

20 

I.I55 

1.058 

LI77 

1.150 

I-I35 

.131 

I.I34    l.°80   1.062 

22 

1.173 

1.064 

LI97 

1.167 

I.I5O 

.146 

I.I49    1-088 

24 

I.I92 

1.069 

I.2I7 

1.183 

I.I65 

.161 

1.165   1.096 

26 

1.075 

1-237 

1.200 

1.181  1.105 

28 

1.258 

1.197  LH3 

30 

1.278 

I.2I4   1-122 

882 


Boiling  Points  of  Solutions.      Table  2<J 


26 

rt  3 


e 

um 


^ 

fco 

•**! 

•si" 

1-8 

7j  O  « 

81 

1« 

||3 

||8 

'§•15 

||D 

2'^ 

-O  re^T 

^•gO 

l|o 

£ 

E-Hs 

ZE 

<'3 

<O3? 

utSw 

Uc^Z 

UO'O 

UCT;2 

KfS^ 

£c«Z 

0 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

2 

1  02 

IOI 

98 

92 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

4 

103 

IOI 

96 

86 

IOO 

IOO 

IOI 

IOI 

IOO 

IOO 

6 

105 

102 

94 

79 

IOI 

IOO 

IOI 

IOI 

IOI 

IOI 

8 

107 

102 

93 

IOI 

IOI 

IOI 

IOI 

IOI 

IOI 

10 

109 

103 

91 

65 

IOI 

IOI 

IOI 

102 

IOI 

IOI 

12 

III 

103 

90 

59 

IOI 

IOI 

IO2 

102 

IOI 

102 

I/j. 

109 

I04 

89 

53 

IOI 

IOI 

102 

103 

IOI 

102 

16 

106 

104 

88 

47 

IOI 

IOI 

103 

103 

IO2 

103  . 

18 

102 

105 

87 

41 

102 

102 

103 

104 

103 

103 

20 

88 

104 

105 

86 

36 

102 

102 

104 

105 

103 

I04 

22 

73? 

104 

106 

86 

30 

I  O2 

102 

105 

105 

104 

105 

11 

59? 
48? 

105 
1  06 

1  06 

107 

85 
85 

25 

20 

103 

103 
103 

1  06 

107 

1  06 
107 

105 

1  06 

1  06 
107 

28 

107 

108 

84 

15 

104 

I04 

108 

108 

107 

108 

30 

m  , 

1  08 

109 

84 

IO 

104 

I04 

109 

.  . 

109 

IIO 

32 

t  m 

109 

in 

84 

5 

105 

105 

III 

.  , 

IIO 

112 

34 

,  . 

IIO 

112 

83 

o 

I  O6 

105 

113 

.  . 

112 

II4 

36 

no 

114 

83 

-5? 

107 

114 

B  , 

114 

116 

38 

.. 

in 

116 

83 

108 

.  . 

116 

.. 

116 

118 

40 

,  , 

112 

118 

83 

.  . 

109 

.  . 

1x8 

.  . 

II9 

120 

42 

.  . 

"3 

1  20 

82 

.  . 

IIO 

.  . 

120 

.  . 

122 

123 

44 

.  . 

114 

122 

82 

.  . 

in 

.  . 

122 

125 

125 

46 

§ 

"5 

124 

82 

9  . 

112 

,  . 

I24 

.  . 

128 

128 

48 

15? 

116 

126 

82 

.. 

XI3 

.. 

126 

.. 

131 

I3l 

50 

^ 

117 

128 

82 

.. 

114 

> 

128 

,  . 

134 

134 

52 

118 

130 

81 

.  . 

115 

I3I 

137 

137 

54 

.  . 

119 

133 

81 

.  . 

116 

.  , 

134 

.  . 

140 

140 

56 

^  t 

119 

137 

81 

,  , 

.  . 

.  . 

138 

H3 

H3 

58 

.. 

119 

139 

81 

.. 

.. 

.. 

146 

146 

60 

M 

1  20 

142 

81 

.. 

1  1 

>  . 

144 

,  , 

I49 

149 

62 

,  . 

120 

145 

81 

.  . 

148 

.  . 

.  . 

64 

.  . 

120 

150 

81 

.  . 

152 

.  . 

66 

llg 

156 

80 

t  m 

.  . 

.  . 

156 

.  . 

.  . 

.  . 

68 

.. 

116 

163 

80 

.. 

.. 

.. 

160 

.. 

.. 

.. 

70 

>a 

170 

80 

.. 

t  f 

m  . 

164 

.  . 

.  . 

.  . 

72 

0  . 

.  . 

176 

80 

.  . 

.  . 

.  . 

169 

.  . 

74 

0  ^ 

183 

80 

m 

t  . 

f  . 

173 

,  . 

.  . 

.  . 

76 

^  0 

190 

80 

.  , 

.  . 

178 

.  . 

.  . 

.  . 

78 

198 

80 

r* 
80 

IOO? 

*yw 

206 

7O 

82 

/y 
7Q 

316? 

84 

225 

/  7 

70 

O 

86 

/  7 

79 

)] 

316? 

.. 

88 

24.8 

QO 
" 

*>4-«J 
26O 

70 

Q2 

274 

/  7 

7Q 

V 

04 

288 

/  V 

78 

96 

40' 

/ 

78 

?8 

** 

T1   • 

3i8 

/ 

78 

ft 

red 

red 

100 

.. 

.  . 

333 

78 

.. 

.  , 

.. 

heat 

heal 

Table  30.          Specific  Heat  of  Solutions. 


883 


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t^oo   i-ifOvnfOvoi-O'-iro       O'HO(s'®:IC<ltOijr)p| 
CJ-OO    ON  ON  ON  O    O    ON  ON  ON     •  35    O;  O^  ON«t    ON  ON  O*  CjN 


q^  q  q"©.  q^  ON  •  qo  o  S  ON  q  ON^C!    •    •  o  ON  •    ^ 


ro  ir^  unco  N  g-oo  roj 

*        *        "        "    l-<     l-<      CJN      * 


O    O 


ON  »-^>3D   t^  ON  HH    M    O'l®  O   t^*O  VO  lO   f>  t~^?O   r^OO  t>»  VO  \O  ^O   t^VO 
ON  OM3S    ON  ON  O   O    ONOi    CTv  ON  q  OCt    Ox  qO5    ON  OCi    q  qOi    0>  qv 


ON3D    ON  ft    H-  flj    tX3D  OO  !>•    C^r>-    t^OO    hsaD   ONOO  OO  OO    fxCO  00 

q>  9t  ON  q  q  05  cx^os  ONOS  ^  qOs  ON  ON  qO5  ON  q>  q\  q  q>  q>  ON 

~O  ON  O  O  O  O  ON  ON  ON  ON30  OO  3D  ON  ON  ON  ON  ON  ON  ON 


•c 

.  o 

:S 

o 

o  o 

•!-!    U 


y 'tjyjifii.il  fij 

p  C0_;       -g  cS  <u  <n 

C/3H  Q        o  G.^  ti 


g 


884    Electrical  Conductivity  of  Solutions.    Table  31 A 


s 


IB 


— — o. 


VO    N  ?O  fOvH    O    -3-®5         O  OC  ^ 

1-1   f»t»         Mt^.jr^^l        ^  Ol  99 


iH  ift  O  O&  *-> 


Oi-OOOO          OMt 

w\o_;>-ir<        CON*. 


ON  M  VO  «*   VO 


\r>  rr>  CT>       00   •-    CTs  ^-vO  GO  ^  OS 


OD  •* 


10  ONfiO 
i-  vo  kO 


00   fO         ^. 


3S 


i-i  r^^H  t^  "I  vo  oo  in  tx  C-*C  ^  CO  e«  CO 


co  o' 


N    «*-iH 
N.    rJ-50 


iH  vo    *J-  vo  O.VO   t^  vo  M    ONOO  VO 


C*>  5.0° 

•vocOvOO   NCOVOVOC*  o'^G 


O    r<    H- 


coo  sc>kO53^CM>c>«ka«o«o;o^**eo^kS9i(NTj<**ei 

covo    rJ-  r*-  T^-  ^-OO  VO 
M   O 


CO  fO  N   N   f<   C«   « 


q  M  «  0- 


OOOOOCOOOOOOOOOOOOO 00000 000         ^^2 

.^ — ^ —^    3  «-• 

Sw 
^  to  e 


d 

' 


. 


" 


t>.  ••*  4  ""'".? 


i« 


Tables  31,  B-D.  Refractive  Indices,  etc.  of  Solutions. 


885 


31.  B.   Refractive  and  Dispersive  Indices  of  Solutions  at  about  18°. 


*§£  2     ^ 


Name  and  Symbol 
Acid,  acetic  HC2H3O2    o  1.333 

„  „  „  201.348 

It  »»  M  40  I«362 

„  ft  I*01 '37  * 

801.378 

v          ?»  v  I0°  T-374 

„  Hydrochloric,HCl  35  1.413 
„  Nitric,  HNO3  501.401 
„  Sulphuric,  H2  SO4  01.333 
„  „  „  201.358 

„  »  »        401.382 

„  „  „         601.410 

801.434 
ioo  1.434? 

01.333 
40  1.358 
ioo  1.360 


Name  and  Symbol 


Alcohol,  (^HgOrf 


.014 

Chloride  Amm.  H4NC1  10  1.351  .016 

t  t 

„           „          „        20  1.370  .018 

,, 

„     Calcium  CaCl2  20  1.384  .019 

•• 

„           „          ,,       40  1.441  .023 
„      Sodium  NaCl  10  1.350  .016 

.017 

„           „          „        20  1.368  .018 

.023 

„     Zinc  ZnCl2       20  1.370  .018 

.024 
.014 

„           „       „           40  1.410  .021 
Hydrate  Potas.  KOH    40  1.403  .018 

.  . 

„     Sodium,NaOH  10  1.359  .016 

.016 

„           „          „        20  1.384  .018 

,  . 

„                „               „           3O    1.404   .020 

.018 

Nitrate  Sodium  NaNO3  20  1-355  -OI7 

.017? 

„           „           „        4°  1.380  .021 

.014 

Sugar,  CiaH^Ou         10  1.348  .015 

.015? 

„                „                20  1.364  .016 

.015? 

„                „                 30  1.381  .017 

31.  C.   Table  for  preparing  Mixtures  of  any  Desired  Strength. 


b  fc|  k 

k  1«|  k 

«3^     o«s  8     %° 

k  l£k 

+J                   C/3                         ,5 

4          £  °  -      PH 

OH           %  °  -1      PH 

PH           £02      PH 

&     £'°~  & 

&     £°~  £ 

O       O.OOO   IOO 

2O     25.000       80 

4O     66.667       60 

60  1  50.00  40 

80  400.00    20 

i      i.oio    99 

21    26.582    79 

41    69.492     59 

61    156.41     39 

81    426.32     19 

2       2.041      98 

22     28.205      78 

42   72.414     58 

62    163.16     38 

82   455.56     18 

3     3.093    97 

23   29.870    77 

43   75439    57 

63    170.27     37 

83   488.24     17 

4     4.167     96 

24   3L579    76 

44   78.571     56 

64    177.78    36 

84    525.00     1  6 

5     5-263    95 

25    33-333    75 

45   81.818    55 

65    185.71     35 

85    566.67     15 

6     6.383     94 

26   35.135    74 

46   85.185     54 

66    104.12     34 

86   614.28     14 

7     7.527    93 

27   36.986    73 

47   88.679    53 

67    263.03     33 

87    669.23     13 

8     8.696    92 

28   38.889    72 

48   92.308     52 

68   212.50    32 

88   733-33     12 

9     9.890    91 

29   40.845    71 

49   96.078     51 

69   222.58    31 

89    809.09     1  1 

IO     II.  Ill      90 

30   42.857    70 

50    100.00    50 

70   233.33     30 

90   900.00    10 

ii    12.360    89 

31    44.928    69 

51    104.08    49 

71    244.83     29 

91  1,011.1       9 

12    13.636     88 

32   47.059     68 

52    108.33    48 

72   257.14    28 

92  1,150.0       8 

13    14.943     87 

33   49.254    67 

53    112.77    47 

73   270.37    27 

93  1,328.6      7 

14    16.279     86 

34   5L5I5     66 

54    117.39    46 

74   284.62    26 

94  1,566.7       6 

15    17.647     85 

35    53.846    65 

55    122.22    45 

75   300.00    25 

95  1,900.0      5 

16    19.048     84 

36    56.250    64 

56    127.27    44 

76   316.67    24 

96  2,400.0      4 

17    20.482     83 

37    58.730    63 

57    132.56    43 

77   334.78    23 

97  3,233-3      3 

18    21.951     82 

38   61.290    62 

58    138.10    42 

78   354.55    22 

98  4,900.0      2 

19   23.457     81 

39   63.934    61 

59    I43.90    41 

79   376.19    21 

99  9,900.0       i 

'20    25.000      80 

40   66.667    60 

60    150.00    40 

80     400.00      20 

IOO        00             0 

31.  D.  Coefficients 

Hydrochloric  Acid 

Hydrate  of  Potassium  .    . 

Sulphuric  Acid 

Nitrate  of  Potassium    .    . 

Common  Salt  . 

Nitrate  of  Sodium  .    ,    . 


of  Diffusion  of  Saline  Solutions  in  Water. 

ooo,  o  ioo  Sulphate  of  Potassium  .  .000,0037 
.000,  0070  Sulphate  of  Sodium  .  .  .000,  0030 

ooo,  0052  Sulphate  of  Magnesium  .  .000,  0020 
.000,0052  Sugar  .........  000,0019 

ooo,  0046  Gum  Arabic     ......  ooo,  ooio 

.000,  0040  Albumen  ........  ooo,  0002 

....  Caramel  ........  000,0001 


886 


Rotation  and  Polarization.     Tables  31,  E-F 


31,  E.   Rotation  in  degrees  of  the  Plane  of  Polarization  for  the  Fraunhofer 

Lines  A— H,   produced  by  passing  through  100  cm,  of  various  solutions, 

containing  in  each  case  1  gram  of  a  given  substance  in  100  en.  cm. 


Name  and  Symbol  of  Substance 

Acid.  Malic.  H2C4H4O5-faq — 

„     Tartaric  H2C4H4O6+aq -f- 


Camphor  Ci0Hi6O  + alcohol." + 

Cholesterine  C^H^O-}- ether 
Cinchonidine  C2o  H  24  N2O-f- alcohol.  .  — 
Cinchonine  C2oH24N2O-f  alcohol.   .  .  -f- 


24 

Glycocol  CH2NH2COOH-f-alcohol.  -f 
Malate  of  Arnmon(H4N)2C4H4O5-f-aq.  — 
Lithium 


Salicihe 
Santonid,  para-; 


Santonine  G15H18O3-|-  alcohol  .....  — 
Sugar  (Cane-)  C^H^On-f-aq.   .  .  .  -- 


milK „  

maltose    ....  „  , 

lactose  .....  „  -j-1 

inverted  ....  „  , 


3.04.2 
2.02.63.2 
ii 
24 
24 

2.22.9 

2.2 


B 


IT 


3.84.8 


C|D 

..0.3 


12 


0.7 
I.O 
10 
10 

15 

16 

6-5 
89 
16 
5.36.65 
5 
5 


8 
2,9 


3.8 


126 


4-9 


167 


22     26 
8.5IO.I 


6.2 


5-7 


H 


13-215.7 


81,  F.    Rotation  in  degrees  of  the  Plane  of  Polarization  for  Fraunhofer 
Lines  A— H  produced  by  plates  of  various  substances  1  cm.  thick. 


Name  and  Symbol  of  Substance 

A 

B 

c 

D 

E 

F 

G 

H 

248 

28 

Chlorate        ,        NaClOa  

24 

^r 

40 

46 

- 

6a 

T^ 

3<X>O 

? 

T.V 

T^ 

. 

168 

?:: 

J97 
146 

246 
178 

? 

? 

Hyposulphate  of  Calcium  CaS2Og.4H2O 

21 

Lead  PbSaOfi^HoO  . 

41 

ce 

77 

89 

„            Potassium  K2S2O6.2H2O   . 

\'m 

T^ 

62 

84 

/  o 

105 

.7 

123 

„            Strontium  Sr  S2  O6.4H2O   . 

t 

16 

lodate  sodium,  per-  NaIO4  

104 

233 

285 

342 

471 

Nicotine  (liquid)  CioH^Ng    — 

127 

157 
108 

Z/i 

173 
? 

16 

217 

D 

275 

327 

425 

511 

Quartz  (ordinary  right  handed)  SiO2  -f- 
Strychnine(sulphate)2C21H22N2O2.H2SO4 

Tartaric  Ether  (liquid)  (C2H5)2C4H4O6  4- 
Turpentine  right  handed  C10Hi6  ...-)- 
w        (liquid)  left  handed  CioHjg  — 

• 

•• 

" 

$ 

"1 

Tables  31,  G-L. 


Miscellaneous  Data. 


887 


81,  G.    Rotation  of  the  Plane  of  Polarization  caused  by  a  Unit  Magnetic  Field 
(C.  G.  S.)  in  Unit  Thicknesses  of  Different  Substances. 

Bisulphide  of  Carbon  (sodium  light)  o°.oo7o    |     Water  (white  light)  ....  o°.oooi 

„  „         „       (thallium    „   )  o°.oo86    ||     Coal  gas o°.ooo,ooo,2 

Note.  In  these,  and  in  nearly  all  cases,  the  rotation  is  with  the  current 
producing  the  magnetic  field.  A  solution  of  ferric  chloride  in  methyl  alcohol  is 
mentioned  as  one  of  the  exceptions  to  this  rule  (Deschanel,  §  839). 

31,  H.    Magnetic  Moment  of  1  cu.  cm.  of  various  substances  (C.  G.  S.) 


Name 
of 
Substance 

Magnetization 
induced  by 
Unit  Field 

Maximum 
Magnetization 

Maximum 
Permanent 
Magnetization 

Name 
of 
Substance 

Magnetization 
induced  by 
Unit  Field 

Iron               . 

300? 
70? 
300? 
140? 

0.2? 

1400 

1400 
800? 
500 

'    <*8oo 

Nickel  Oxide 
Water  .... 
Bismuth  .  .  . 
Phosphorus  . 

+  0.1? 

—  o.oi  ? 

—  0.01? 

—  0.004  ? 

Steel  
Cobalt.  .  .  . 
Nickel  .... 
Iron  Oxide    . 

81,  I.    Coefficients  of  Friction  (f)  for  -water  corresponding  to  Velocities  (v)  in 
centimetres  per  second  (From  Weisbach). 


V 

/ 

V 

/ 

V 

/ 

•v 

/ 

V 

/ 

o 

00 

100 

.00299 

200 

.00264 

300 

.00249 

400 

.00239 

IO 

.00554 

no 

.00293 

210 

.00262 

3IO 

.00248 

410 

.00239 

20 

.00445 

I2O 

.00288 

220 

.00260 

320 

.00247 

420 

.00238 

30 

.00396 

130 

.00284 

230 

.00258 

330 

.00246 

430 

.00238 

40 

.00368 

140 

.00280 

240 

.00256 

340 

.00245 

440 

.00236 

50 

.00347 

150 

.00276 

2SO 

.00255 

350 

.00244 

450 

.00236 

60 

.00333 

IOO 

.00274 

200 

.00254 

360 

.00243 

460 

.00235 

TO 

.00321 

170 

.OO27I 

270 

.00253 

370 

.00242 

470 

.00235 

80 

.00312 

180 

.00269 

280 

.00251 

380 

.00241 

480 

.00234 

90 

.00305 

190 

.00266 

290 

.00250 

390 

.00240 

490 

.00234 

100 

.00299 

200 

.00264 

300 

.00249 

400 

.00239 

500 

.00233 

31,  J.  Coefficients  of  Friction  of  Solids  on  Solids. 

Oak 

Hard 
Wood 

India 
Rubber 

Leather 

Hemp. 

Bronze 

Iron 

Cast 
Iron 

Oak 

.2—  .5 

.38 

.% 

.52 

.48 

.40 

16 

.16 

,iq 

Bronze          

48 

.20 

.18 

.21 

Iron  (cast,  smooth)  . 
„         „     wet  .  .  . 
„         „     greased  . 

49 

% 

•• 

.20 

"i 

.15 

.08 

.2 

.31 

.15 

.2—  .4 

.2—  .4 
•31 
•15 

81,  E.    Action  of  Plates  (1  cm  thick  and  bounded  by  plane  surfaces)  upon  nor- 
mally incident  Radiant  Heat. 


Substance 

Re- 
flects 

Ab- 
sorbs 

Tmi?sSl          'S^stance 

Re- 
flects 

Ab- 
sorbs 

Trans- 
mits 

1 

'& 

1 
E 

£ 
tt 

0 

55 

Lampblack.  .  .  . 
India  Ink 
Ice                     .  . 

^  A.  A. 

O  v>rHO  rtOOOO  OOO  O  O  THOOO  O 
•^t-  <X)  "-< 

100% 

95 
91 
§6 

£6 
62 

47  ^ 

20? 
0 

100 
100 

96 

94 
92 

00 

0% 

o 

g; 

0 

30 
45 

0 

92 

0 
0 

o 

0 
0 
0 

Steam  Heat  White  Heat 

Water  

4% 
4 

1 

6 
6 

12 

75? 
8 

9 

o 

0 

86% 
75 

i 

Sj 

20? 
0? 
0  —  IO? 
0—  .02  > 

10% 

10 

13 

20 
21 
25? 
30 

53 

0 

20 
0 
0 
%92 

QO?—  100 
QQ.Q8H- 

Aque  ousSolutions 
Alcohol   

Ether.  . 

White  Lead  .  .  . 
Glass  

Oils  

Chloroform  .  .  . 
Turpentine.  .  .  . 
Bisulphide  Carbon 

Shellac  

Polished  Metals  . 
Rock  Salt 

Lampblack.  .  .  . 
White  Lead  .  .  . 
Ice     

fShellac.  .  .... 

Mercury  .  .      . 

Polished  Metals  . 
Rock  Salt  .  .  .  . 
Vapors  at  i  cm  . 
Perm.  Gases  76  cm 

Glass  

India  Ink.  . 

31,  L.  Estimates  of  the  number  of  Units  of  Heat  radiated  in  1  sec.  by  1  sq.  cm. 
blackened  surface  in  space  at  0°. 

Temp.Rad.  I  Temp.Rad.  jTemp.  Rad.jTemp.  Rad.jTemp.  Rad.f Temp. Rad.|  Temp.  Rad. 


— 273°—  .oi9?i-Mco°-Koi2?*|  500°  .1? 
—2oo°— .015?  200°  .028?*!  boo0  .2? • 

— 100°— .009?   300°  .05?*  I  700°  .2?' 

0°  .000  I  400°  .08?*  I  &oo°  .3?! 


900°  .5? 

1000°  .-]> 

1100°  .g>//\  i 
1 200°  i. 2? f§| 


I3000  2?**  1700°  5? 
I4000  2?"  1600°  7?' 

"3?     11900°  10? 
4?     I  2000°  13? 


2500°    60  ?t* 
5000°  270? f* 

3500°  1200  ?§§ 

£000°  5400  ?ss 


*  Dark. 
"  "White  Heat11 


f  Dull  red. 
,    it  Flame. 


§*  "Red  Heat".    §  Cherry  Red.    //  Orange.    f§  Yellow 
f*  Voltaic  Arc  Light.    §§  Sunlight 


888 


Heat  of  Combustion. 


Tables  32-33. 


32a.    Heats  of  Combustion  in  Oxygen. 

Name 
of  Substance 
Consumed. 

Chemical  Reaction 
involving  16.0  grams  of  Oxygen 
in  each  case. 

Grams  of 
Substance 
consumed. 

Grams  of 
Product 
formed. 

Units  of  Heat 
developed. 

Units  of  Heat 
per  gram 
consumed. 

UH 

tflli 

J1I.18 

Jj  IMI 

Acetylene.  .... 

2  Q  Ha      4-  5  O2  =  4  CO2  4-  2  H2  O 
C2H6O4-  3O2=  2CO2  +  3H2O 
As4         4-30*  —  2As2O3 
As4         4-  5O2=  2As2Os 
2  Ba          4-      O2  =  2  Ba  O 
Bi4          4-  30a=  2BiaO3 
2Ca          4-     O2=  2CaO 
C           4-     O»=     COj 
2  CO         4-     O,=  2CO2 

2C1,              4-        02=    2C1.0 

4Cu          4-     Oa=  2Cu,O 
2Cu          4-     O,=  2CuO 
2C2H6      -f-  7O2=  4CO24-6H,O 
C4H,0O4-  6O3  =  4CO24-sH2O 
2C2H4      4-  6O»=  4CO24-4H2O 

2H,              4-       O2=    2H2U 
2L                 4-    50a=    21,0, 

2Fe           4-     Oa=  2FeO 
3Fe           4-  2O2=     Fe3O4 
2Pb           4-     O2=  2PbO 

2N2              4-       O2=   2N9O 

N2           4-     O2=  2  NO 
Na            4-   202=  2  NO, 
P4              4-    50a=    2P205 
2K2            4-      O2=  2K2O 
Se,          4-  202=  2SeO, 
2Ag2         4-     O2=  2Ag2O 
2  Naa         4-     O2  =  2  Na2  O 

2Sr           4-     O,=  2SrO 
CS2         4-  3O2=     CO,4-2SOi 

S,                 4-    2O2  =    2SOa 
2T12             4-       O2=    2T12O 

2Sn           4-     Oa=  2SnO 
2Sn           4-  2O2  =  2SnOa 
C10H16    4-i4O2  =  ioCO24-8HaO 

2  Zn          4-     Oa  =  2  Zn  O 
32b.    Heats  of  Combustion  in 

5.2 

7-7 
50.0 
30.0 
136.8 
138.7 

39.9 
6.0 
28.0 
70.7 
126.3 
63.1 

ti 

4-7 

2.0 

50.6 
55-9 
41.9 
206.4 
24.0 
399-6 
199-8 
4.0 
28.0 
14.0 
7.0 
12.4 
78.1 
39-4 
215.4 
40.0 

87.3 
12.7 
16.0 
408.0 
118.0 
59-0 
4-9 

67.9 
Chloi 

21.2 

46io 

152.8 
154.7 
55.9 
22.0 
44.0 

86.7 
142.2 
79.1 
20.3 

22.2 
20.6 

18.0 
66.6 
71.9 
57-9 

222.4 

40.0 

415.6 
215.8 

20.0 
44.0 
30.0 

23.0 

28.3 

94-1 
55-4 
231.4 
62.0 

103.3 
28.6 

32.0 

424.0 

134.0 

75-0 

20.8 

80.9 

ine. 

62,OOO 

54,000 

44'ooo 
130,000 
13,300 
130,000 
48,000 
67,000 
—  18,000 
40,000 
38,000 
54,000 
50,000 
56,000 
69.000 
9,000 
75,000 
66,000 
50,000 
146,000 
42,000 
30,000 
52,000 
18,000 

—  22,000 
—  1,000 

71,000 
136,000 
29,000 

5,800 

152,000 

131,000 

43,000 

36,000 
42,400 

m 

5^000 

12,000 

7,000 
1,030 
1,460 
950 
06 
3,28o 
8,000 
2,400 
-  250 

12,500 
9,000 

12,000 
34,500 

1/7 
1350 
1575 
243 
6,100 
105 

153 
13,100 
-650 
-1550 
-  150 
5750 
1745 
730 

27 

3,3oo 
10,300 
9,700 
1,500 
3,400 
2,250 
104 

!575 
1,230 
10.700 
10,500 
4,cx» 
1,300 

500 

200 

40 

§1 

334 

100 
—10 

13 
25 
520 
375 
505 
M40 

10 

255 
4«4 

550 

I 

240 
73 

63 
142 
94 
4-3 

24 

54 

1.49 

Alcohol  

Bismuth    

Carbonic  Oxide    . 

oooer 

Ether  

Hydrogen.  .  .  . 

Lead  

Magnesium  .... 

Methane    .  . 

"             * 

Phosphorus.  .  .  . 
Potassium    .... 
Selenium  

tilver  

Spermaceti  .... 
Stearine. 

§trontium  

ulphideCarbon,Bi- 

Thallium  . 

Tin  

Turpentine  .... 
Wax   . 

Wood  

Zinc    

Name 
of  Substance 
Consumed. 

Chemical  Reaction 
involving  70.7  grams  of  Chlorine 
in  each  case. 

o-g* 

w  1, 

hi 

i! 

jit 

!* 

M 

II 

llfi 

o  S 
£  > 

14 

Units  of 
per  gr 
consurr 

Antimony  

As4  4-  6  Cla  =  4  As  C13 
Cu4-    Cl,=    CuCl, 
H2  4-    C12  =  2HC1 
2Fe  4-3Cla=    Fe2Cl6 
Ka  4-    C12  =  2KC1 
Sn  4-2Clt=    SnCU 
Zn  4-    C12=    ZnCl2 
33.    Heats  of  Combinati 

80.7 

2.0 

59-0 
64.9 
on. 

151.4    57,000)    707 

i2o.6|    50,000      904 
133.8    oi,ooq     960 
72.71     47,000  23,500 
io8.0|    65,000    1,750 
148.8!  207,000  2,650 
129.7)    64,000    i,  080 
135.6]    99,000!  1,530 

301.23 
421.08 
401.33 
9801.01 
73,1.40 
110.4.48 
451.38 
6412.15 

Arsenic 

Hydrogen  

Iron       ...         . 

Potassium    .... 
Tin  

Zinc   

Name 
of  Substance 
Acted  upon. 

Chemical  Reaction 
involving  16.0  grams  of  Oxygen 
or  its  equivalent. 

£•2  c 
««S8 

j|j 

Units  of  Heat 
developed. 

111  In!! 
pipjli 

Copper        .  . 

2  Cu4-O24-2SOo,4-Aq  —  2CuSO4'Aq 

63-1 
60.0 
47.0 
04.9 

159.1      54,200s1     86o|  36  Ii.i7 
94.  d     30,300)     6ooj  25  0.78 
63.0     i8,3od     qox),  ib  (0.40 
160.9!    108.5001   1.6701  70  12.35 

Nitric  Oxide  .  .  . 
Nitrous  Acid  .  .  . 
Zinc   

Table  34. 


Electromotive  Force. 


umuijBjj 


ssBjg 


UOJJ 


•"O 


'O 
'S 


'X'tV 

70si 


»/o  <* 


%og 


vn  LO  r>  oo   t^  o\^O  oo    -  . 

O  OO  I-H    O\  t^vO    PO  M    fi  ^    >->    ••*    PO 

'  I        7  I  f  f  I  f  I 


'o^-q  *•>  oo  r^.^^-'-'  oo  N  POPOM 


J_LLIJ_L 


2_|i 


_          OO  OO    M 

rorf  Cb<b^t-rooOOr^«i- 

IT LI  r  f  f 


\r>  ^t-  o    «    PO 

O  rh  O   O   i-* 

O  t^vO    ^  PO 


-    _     _  _      3-\O  OO    O    •<*• 

VO  O  t^vO    ^  POO  O   i-    PO  rhirj  i-. 

U JLLLL       '  '  '  ' 


s 


IT 


II 


If       ^rTc? 

'  f  r 


•*i-  r-^.  PO  ^  M  ^  LOOO        o  oo   ON      oo 

^-  u->o   ^-NONMO        O  10^         -^ 

O    ~    PO  rt  t-xOO  00    -    CJ  I-H  PO  •=*•        00 


vO    ON  >O  PO  ^  t>> 
oo  PO  rl    1T5  <-    M 

u->  i-c  r-i  \o  o  "-1 


•£  a 


N 


O\       OO    PO 
O          N    ^- 


0^0^%- 

t^flj 


"c1*- 


ppy 

ounqd[ns   c^ 


890 


Electromotive  Force.    Tables  35— 3f> 


SJJOA  tn 

>o 

^        JJJ 

f?00   CO    M    *• 

rj     i_i     o     i-1     <^.    r>     fO 

33JOJ  9AIJ 

-ouioxioafg 

ON 

»    CO      rl- 

0* 

o     o     S" 

3-Sax 

O                   #v 

ft     R  w> 

^-^       R     R     R 

R     R     R     R     R     R     R 

0 

**-    fl 

>> 

^ 

CS    6    G    . 

;|  ^ 

j  .g 

S     R   5£ 

V 

0    3    0    £ 

s   i    R-P  .S  •£  > 

(2  ^ 

el  U 

0? 

.  g.  ,  «  s 

c3  ^   c3  -"-3 

^suCO 

# 

1 

i 

CL 

"I 

!  1 

h   S        « 

J 

Solution  next 
Positive  Pole. 

rmanganates(withM 
re  Nitric  Acid 

7o 
;hromates 
Iphate  of  Mercury  (] 

0,     R     C     R 

a 

R  o    R   -    c 

*3 

c/D 

R  --5 

»»  »>  » 
»  »  » 
/o  Nitrate  of  Coppe 
Iphate  of  Mercury  (] 
trie  Acid 
wdered  oxides  Mang 
ver  Chloride 

*0 

QJ      3 

o  --5    3 

^•\       R      S5     J^ 

£      S5   ^N     ij   **5     Q   *"^ 

> 

eu  ex  v 

o  OQ  C/D 

ro 

S>OD  Z  CL  c/D 

rf 

S 

oo 

§ 

| 

c& 

e    1 

| 

85.  Electromotive  1 

Solution  next 
Negative  Pole. 

rate  of  Potassium. 
Sulphuric  Acid. 

3 

NJ 

co 

t  »  »  W 

Sulphuric  Acid. 

»  » 
Sulphate  of  Zinc. 

»  »  »> 

•|     1  ? 

r   "."iSJ^  S 

o  rrj    o  <j 
r    =<'S<2    , 

lala  ' 

-  "-io-as  s 

1616 

5 

COT 

T3  ^o 

JX 

^0  ^0  _0  ^0 

o    o    o    o    o    o 

Ofl 

ffi°a 

C£ 

so^°-  - 

tVs>1?Vs 

. 

bb  o 

o 

.a 

S| 

1« 

O 

N             o 

1 

Iff 

"w     ^ 

R     C     R 

~   ^   ^  a    - 
~N     ' 

R     R      S   bJQ      R      R.S 

re             N 

•H 

<u  g 

o  6 

a 

4 

^ 

(X  <i 

<J 

co 

<u 

CX75 

o 

.HH*                          ,         '§ 

I 

0)  £3 

i—  J    P  H     = 

c    SS           Jd  3 

O 

"  —  i  G 

_, 

au 

* 

2 

|| 

"1 

'oj 

'S     £    c    R 

-  rt 

«  «  *fi!g 

^5^1 

86.  Electromotive  Force 

in  Volts 

and  Striking 

Distance  in  Millimetres. 

mm. 

.0 

.1   |  .2 

.3 

•4 

.5 

.6 

•7 

.8 

•9 

0 

I 
2 

3 

0 

434° 
7600 
10320 

500 

4700 
7890 
10580 

1000 

5050 
8170 
10830 

1470 

5400 

8450 

11080 

1920 

5740 
8730 

11320 

2360 
6070 
9000 
11560 

2780 
6390 
9270 
11800 

3r9° 

6700 

9540 
12040 

3580 
7000 
9810 
12270 

3960 
7300 
10070 
12500 

The  values  in  this  table  are  subject  to  a  probable  error  of  about  100  volts. 


Tables  37—38.          Specific  Resistance. 


891 


37a.    Specific  Electrical  Resistances  of  Conductors  at  0°. 

Resistance       Resistance       Resistance 

of  a 

centimetre- 
cube  in 
microhms.* 
•  1.50* 

1. 60 


Per  Cent  of 

Increase 
per  degree 
centigrade 


Name 

of 

Substance 

Silver,  annealed    ....  1.50*  0.019  0.16             0.377 

,,       hard  drawn  .  . 

Copper,  annealed.   .   .   .  1.58  0.020  0.14             0.388 

hard  drawn  .   .  1.61  0.020  0.14 

Gold,  annealed 2.0  0.026  0.39             0.365 

,,       hard  drawn    ...  2.1        .      0.026  0.41 

Aluminum  annealed    .   .  2.8  0.036  0.07 

Brass 5.5  0.070  0.46 

Zinc,  pressed 5.6  0.073  0.40             0.365 

Platinum,  annealed.    .  .  9.0  0.115  1.90 

Iron,  annealed 9.5  0.121  0.74 

Gpldfe)  Silverd)  alloy    .  10.9  0.138  1.65             0.065 

Nickel,  annealed  ....  12.4  0.157  i.io 

Tin,  pressed 13.0  0.166  0.95             0.365 

Lead,      , 19.0  0.242  2.16             0.387 

German  Silver 20.8  0.265  1.77             0.044 

Platinum(2)Silver(j)  alloy  24.0  0.306  3.3?             0.031 

Antimony 35.2  ..  2.36             0.389 

Mercury  (liquid)   ....  94.2  ..  ..              0.072 

Bismuth 130.0  1.656  12.7             0.354 

Electric  Light  Carbons  . 

(about) 6000. 

*  These  results  must  be  multiplied  by  1000  to  reduce  them  to  the  C.  G.  S.  system 
37b.    Specific  Electrical  Resistances  of  Insulators. 


Name  of  Substance 

Resist,  in  Ohms  of  a  centimetre-cube  f 

%  increase  per0. 

Selenium  

(about)               60  ooo 

-4-  I 

Gutta  Percha  .... 
Shellac  

„        7,  ooo,  ooo,  ooo,  ooo,  ooo. 
,,         9,  ooo,  ooo,  ooo,  ooo,  ooo. 

—  10? 

„       30,  ooo,  ooo,  ooo,  ooo,  ooo. 

Paraffme    

„      30,  ooo,  ooo,  ooo,  ooo,  ooo. 

Glass   

Greater  than  any  above. 

sreat  negative. 

Air  and  other  Gases. 

Practically  Infinite. 

t  These  results  must  be  multiplied  by  i,ooo,ooo,dbo  to  reduce  them  to  the  C.  G.  S.  System 
88.    Specific  Electrical  Resistance  in  Ohms,  of  a  Centimetre-cube  of  different 
Electrolytes  (see  Table  31). 


Per 

Cent. 

% 

Hydro- 
chloric 
Acid,  HC1 

Nitric 
Acid. 
HNO3 

Sulphuric 
Acid 
HaS04 

Sulphate 
of  Copper 
CuS(54 

Sulphate 
of  Zinc 
ZnS04 

Chloride 
Ammonium 
H4NC1 

Ch^ride 
Sodium 
NaCl 

5 

2.6 

3* 

5-o 

56.0 

55-0 

11.6 

1  6.0 

10 

.6 

2.2 

2.6 

33-° 

33-0 

6.0 

9.0 

'5 

•4 

.6 

1.9 

25.0 

26.0 

4.0 

C.5 

20 

•3 

•4 

•5 

20.0 

23.0 

3-2 

5-5 

25 

•4 

•3 

•4 

22.5 

2.8 

5-o 

30 

•5 

•3 

•4 

.  . 

250 

35 

•7 

•3 

•4 

30.0 

40 

2.0 

•4 

•5 

45 

.5 

.6 

1° 

.6 

9 

60 

2.0 

2.7 

1° 

2-5 

4.8 

80 

3-7 

9.0 

90 

IO.O 

100 

12.5 

Note.  The  results  m  this  table  must  be  multiplied  by  1,000,000,000  to  reduce  them  to 
the  C.  G.  S.  System.  They  are  intended  to  be  accurate  at  about  18°,  but  are  subject  to  a 
probable  error  of  about  10%.  See  Table  31. 


892 


Arbitrary  Scales.         Tables  39-41. 


89  —  Fahrenheit  and  Centigrade  Thermometers. 


c. 

F. 

C. 

F. 

C. 

F. 

G. 

F. 

C. 

F. 

G. 

F. 

G. 

F. 

G.  IF. 

-125 

-193.0 

0 

32.0 

25 

77.0 

50 

122.0 

75 

167.0 

IOO 

212.0 

225 

437-0 

350  662 

120 

184.0 

I 

33-8 

26 

78.8 

5i 

123.8 

76 

168.8 

105 

221.0 

230 

446.0 

400  752 

"5 

175-0 

a 

35-6 

27 

80.6 

52 

125.6 

77 

170.6 

no 

230.0 

235 

455-0 

45°!  842 

no 

1  66.0 

3 

37-4 

28 

82.4 

53 

127.4 

78 

172.4 

"5 

239.0 

240 

464.0 

500 

932 

105 

I57.o 

4 

39.' 

29 

84.9 

54 

129.2 

79 

174.3 

120 

248.0 

245 

473.o 

550 

1022 

IOO 

148.0 

5 

41.0 

30 

86.0 

55 

I3I.O 

80 

176.0 

125 

257.0 

250 

482.0 

600 

III2 

95 

139.0 

6 

42.8 

3i 

87.8 

56 

132.8 

81 

177.8 

130 

266.0 

255 

491.0 

650 

1202 

90 

130.0 

7 

44.6 

32 

89.6 

57 

134.6 

82 

179.6 

r35 

275-0 

260 

500.0 

700 

1292 

85 

1  2I.o 

8 

46.4 

33 

91-4 

58 

136.4 

83 

181.4 

140 

284.0 

265 

509.0 

750 

1382 

80 

1  1  2.0 

9 

48.2 

34 

93.« 

59 

138.8 

84 

I83.a 

H5 

293.0 

270 

518.0 

800 

T472 

75 

I03.o 

10 

50.0 

35 

95-0 

60 

140.0 

85 

185.0 

150 

302.0 

275 

527.0 

850 

1562 

70 

94.0 

ii 

51.8 

36 

96.8 

61 

HI.8 

86 

1  86.8 

155 

3II.o 

280 

536.o 

900 

1652 

65 

85.0  12 

53-6 

37 

98.6 

62 

143.6 

87 

188.6 

1  60 

320.0 

285 

545.o 

950 

1742 

60 

55 

76.0 
67.0 

^3 

M 

55-4 
57-» 

38 
39 

100.4 
102.3 

63 
64 

145-4 
147-a 

88 
89 

190.4 
192.3 

165 
170 

lit 

290 
295 

554.o 
563.0 

1000 

1050 

1832 

1922 

50 

58.015 

59«° 

40 

104.0 

65 

149.0 

90 

194.0 

175 

347.0 

300 

572.o 

I  IOO 

2012 

45 

49.0 

16 

60.8 

4i 

105.8 

66 

150.8 

9i 

195.8 

1  80 

356.0 

305 

581.0 

1200 

2192 

40 

40.0 

17 

62.6 

42 

107.6 

67 

152.6 

92 

197.6 

185 

365.0 

310 

590.0 

I30O 

2372 

35 
30 

3i.oji8 

22.019 

64.4 
66.a 

43 

44 

109.4 

I1I.2 

68  154.4 
69  156.3 

93 
94 

199.4 

201.2 

190 
T95 

374-0 
383.0 

315 

320 

599.0  1400 
608.0  1500 

2552 
2732 

25 

I3.o|20 

68.0 

45 

113.0 

70 

158.0 

95 

203.0 

200 

392.o 

325 

617.0  1600 

2912 

20 

-4.0 

21 

69.8 

46 

114.8 

7i 

159.8 

96 

204.8 

205 

401.0 

330 

626.0  1700 

3092 

15 

+5.o 

22 

71.6 

47 

II6.6  72 

161.6 

97 

206.6 

2IO 

410.0 

335 

635.0  1800 

3272 

10 

+14.0 

23 

73-4 

48 

H8.473 

163.4 

98 

208.4 

215 

419.0 

340 

644.0  1900 

3452 

5 
—  o 

+23.0 
4-32.0 

24 

25 

75-a 

77.0 

49 
50 

120.274 
I22.o||75 

165.8 
167.0 

99 

IOO 

210.3 
212.0 

220 
225 

428.0 
437-o 

345 
350 

653.0  2000 
662.o|2IOO 

3632 
3812 

40.   Hydrometer  Scales. 


41.    Wave-lengths  in  Air. 


1    » 

.2* 

CJ 

1 

12 

'5 

S       £ 

w 

c 
.2 

§ 

U 

Wave- 

f 

a 

S3 
?« 

• 

S 

« 

1 

T3 
CO 

O 
3  « 

CO 

G 

ja 

0 

- 

"c 
u 

i 

Length 

32 

tt.S 

II 

O 

M 

o 

3 

£3 

| 

Q 

3 

3 

S 

pa 

1 

cm. 

0 

I.OOO 

I.OOO 

I.OOO 

I.OOO 



K« 

K 

__ 

17 

383!  .00007685 

5 

1.035 

1.030 

.971 

1.025 

A 

— 

— 

— 

18 

404]  .00007605 

10 

1.073 

1.  030 

1.062 

.944 

1.050 

B 

— 

— 

Red 

28 

593 

.00006870 

15 

1.114 

.967 

1.097 

.919 

.970 

1.075 

— 

Lia!Li 

— 

32 

645 

.00006708 

20 

1.158 

.936 

1.133 

.895 

.936 

I.  IOO 

G 

H« 

H 

mm, 

34 

694 

.00006563 

25 
30 

1.205 
1.257 

.907 
.880 

s; 

.872 

.850 

.905 
.876 

1.125 
1.150 

D,\ 
Djl 

Na 

Na 

Yellow 

50 

/i  003 
11007 

.00005896 
.00005890 

35 

1.313 

.854 

1.259 

.829 

.849 

1.175 

— 

— 

Tl 

Green 

68 

— 

.00005350 

40 

1.375 

.830 

1.308 

.810 

.824 

1.200 

E 

— 

— 

— 

71 

1523 

.00005270 

45 

1.442 

.807 

1.360 

•791 

1.225 

F 

H/9 

H 

— 

90 

2080 

.00004862 

50 

1.517 

.785 

1.417 

.773 

1.250 

— 

Srd 

Sr 

Blue 

105 

2386 

.00004607 

55 

1-599 

.764 

1.478 

.756 

L275 

f 

Hy 

H 

— 

127 

— 

.00004341 

60 

1.691 

•745 

1.545 

.739 

1.300 

G 

— 

— 

128 

2854 

.00004309 

65 

1-795 

1.619 

-723 

1.325 

g 

— 

Ga 

— 

135 

2870 

.00004227 

70 

1.912 

1.700 

.708 

1-350 

lid 

H 

Violet   151 

— 

.00004102 

75 

2.045 

1.790 

1-375 

— 

KB 

K 

—     1153 

— 

.00004060 

80 

1.400 

Hj\ 

TT 

Ga 

— 

162 

— 

.00003969 

IOO 

i 

1.500 

Ha/ 

" 

1  66 

~ 

.00003934 

Tables  42— 43.       Arbitrary  Scales.  893 

42.  a.  English  Board  of  Trade  (Imperial)  Wire  Gauge. 


.8  a    2  i   N°-  Diam-  N°. 

C.I       &S        i    0.762      n 
fa         U         2      .701       12 

Z°      5£       3     -640     13 
7/0     1.270      4     .589     14 
6/0      1.179      5     .538      15 
5/0     1.097      6     .488     1  6 
4/0     1.016      7     .447      17 
3/0       .945      8     .406     1  8 
2/0       .884      9     .366     19 
o       .823    10   0.325     20 

Diam. 

0.295 
.261 

.234 
.203 

.183 
.163 
.142 
.122 
.102 

No.   Diam.      No.  Diam.      No. 
21    .0813       31    .0295       41 
22    .0711         32    .0274        42 

23   .0610      33    .0254      43 
24   .0559       34    .0234       44 
25    -0508      35    .0213      45 
26   .0457      36   .0193      46 

27   -0417      37    .0173      47 
28    .0376      38   .0152      48 

29   .0345      39   -OI32      49 
30   .0315      40   .0122       50 

Diam 
.0112 
.OIO2 
.0091 
.0081 
.0071 
.0061 
.0051 
.0041 
.0031 
.0025 

42  b.  Birmingham  Wire  Gauge  (B.  W.G.) 

No. 

Diam. 

No. 

Diam. 

No. 

Diam. 

No. 

Diam. 

I 

SB 

og 

i 

0.80 

IO 

0-35 

19 

O.IIO 

28 

0.037 

* 

1 

|.s 

2 

•74 

II 

•32 

20 

.09! 

29 

.°34 

oO 

IS 

3 

.68 

12 

.28 

21 

.083 

30 

.031 

A 

g 

rt.H 

4 

.62 

13 

.25 

22 

.0/3 

31 

.026 

QJ> 

5 

•57 

14 

.22 

23 

.065 

32 

.023 

oooo 

1.2 

6 

•53 

15 

.19 

24 

.057 

33 

.021 

ooo 

I.I 

7 

.48 

16 

25 

.051 

34 

.018 

00 

1.0 

8 

43 

17 

.15 

26 

.046 

35 

.013 

o 

0.9 

9 

0-39 

18 

0.13 

27 

0.041 

36 

O.OIO 

43.  Musical  Pitch 

(Tempered  Scale—  complete  Vibrations  per  second). 

Physical 

32  foot 

ififoot    Great 

Little 

2  foot 

i  foot 

6  inch 

3  inch 

t;   "^ 

Pitch 

Octave 

Octave  Octave 

Octave   Octave 

Octave 

Octave 

Octave 

G 

1  6.0 

32.0 

64.0 

128.0 

256.0**    512.0 

1024 

2048 

§Jr  g 

I6.5 

32.9 

65.9 

I3I.8 

263.5*'' 

"  527.0 

1054 

2108 

U~,« 

G# 

17.0 

33-9 

67.8 

135-6 

271.2**    542.4 

1085 

2170 

G 

17.4 

34-9 

69.8 

139.6 

279.2 

558.3 

1117 

2233 

D 

18.0 

35-9 

71.8* 

143.7 

287.4| 

574-7 

1149 

2298 

c# 

18.5 

37.0 

73-9* 

147.9 

59L5 

1183 

2366 

D:# 

19.0 

38.1 

76.1* 

152.2 

3O44J 

608.9 

1218 

2436 

D 

19.6 

39-2 

78.3 

156.7 

3134 

626.7 

1253 

2507 

£ 

2O.2 

40-3 

80.6 

161.3 

322.5 

645.1 

1290 

2580 

D# 

20.7 

41.5 

83.0 

166.0 

332.0 

664.0 

1328 

2656 

F 

21.4 

42.7 

854 

170.9 

34L7 

683.4 

1367 

2734 

£ 

22.0 

44-0 

88.0 

175.9 

35L7 

703.5 

1407 

2814 

F# 

22.6 

45-3 

90.5 

181.0 

362.0 

724.1 

1448 

2896 

F 

23.3 

46.6 

93-2 

186.3 

372.6 

745-3 

1491 

2981 

G 

24.0 

47-9 

95-9 

191.8 

383-6 

767.i§  1534 

3068 

F# 

24.7 

49.4 

98.7 

1974 

394-8 

789.6* 

i  1579 

3158 

G4I1 

25.4 

50.8 

101.6 

203.2 

406.4 

8i2.8£ 

f  1626 

3251 

G 

26.1 

52.3 

104.6 

209.1 

418.3 

836.6 

1673 

3346 

A 

A# 

26.9 

27.7 
28.5 

53-8 
55-4 
57.o 

107.6 
no.  8 
114.0 

215-3 

221.6 

228.1 

430.5tf  861.1 
443,2ft  886.3 
456.1ft  912.3 

1722 

1773 
1825 

3444 
3545 
3649 

A 

29.3 

58.7 

117.4 

234.8 

469.5 

939-0 

1878 

3756 

B 

30.2 

60.4 

120.8 

241.6 

483.3 

966.5 

1933 

3866 

A# 

3**1 

62.2 

124.4 

248.7 

4974 

994.8 

1990 

3979 

32.0 

64.0 

128.0 

256.0 

512.0 

1024.0 

2048 

4096 

B 

Note.  The  Paris  Conservatoire  standard  of  pitch,  recently  adopted  by 
the  International  Congress  at  Vienna,  is  435  vibrations  per  second  for  the  note 
A  of  the  treble  staff.  This  gives  C=26i  on  the  natural  scale.  American  instru- 
ments tuned  to  Concert  Pitch"  give  C  =-•  270  -K 

p.          lih^6,?1  P»   of  ^ass  Voice<    **  Middle  C  of  Piano,    f  Lowest  D  of 
Flute,    ft  Violin  A.    §  Highest  G  of  Treble  Voice. 


894  Astronomical  Tables.       Tables  M  A.— E. 

'« w  ^^Erspco       5 


Thousandths  of  degrees. 


Thousandths  of  degrees. 


,2  Thousandths  of  degrees. 

€  9&ft3;ft3$^^Sg|&&8£ 

|   q\q  «oo  f  ovq  ejoo  ^qvq  «oq  -t-qvq  « 


O       •-• 


Thousandths  of  degrees. 


§  Thousandths  of  degrees. 


-'   O 


-I? 


©oooo 


oooo 


ts  2 


««-> 
«f 

C   d 


^°S^C2^  5-3 

rji  .- <    rj 

^-T>  S    O 


Thousandths  of  degrees.  ^ 

888«*8TS^WS^SSr»S^rs«&  5- 

qvq«: 


« 


o'ooooooooo 


--* 


-.,    1    | 


Tables44,F— G. 


Astronomical  Tables. 


895 


44,  F.  Declination  of  the  Sun  in  Degrees  at  Greenwich  Mean  Noon  for  1891. 

Day   Jan.      Feb.      March    April     May      June      July     August     Sept,      Oct.      Nov.     Dec,    Day 


0  23.091 

1  23.01 1 

2  22.925 

3  22.831 

4  22.729 

5  22.619 

6  22.502 

7  22.378 

8  22.246 

9  22.108 

10  21.961 

11  21.808 

12  21.648 

13  21481 

14  21.306 

15  21.125 

16  20.938 

17  20.743 

18  20.542 

19  20.335 

20  20.121 

21  19.901 

22  19.675 

23  19443 
*24  19.204 

25  18.960 

26  18.710 

27  18455 

28  18.194 

29  17-927 
140  17.653 
31  17-378 


17-378  -7-958   4-157 

17-096  7-579 

i6.8og  7.199   4. 

16.516  6.816   5.312 

16.219  6432 

15.918  —6.046    6.074 

15.611  5-659   6.453 

15.301  5.271    6. 

14-986  4-8&I    7- 

14.666  4-491    7-5 

14.343  —4/J99 

14.016  3.707    8.31 

13.684  3-314 

13.350  2.920 

13.011  2.525    9409 

12.669  —2.131    9.768 

12.324  1.736  10.124 

11.975  1.341  i 

11.623  0.945  i 
11.269 


io£ii  —0.155 
10.551  +0.240 
10.188  0.635 
9.822  1.029 
9454  1423 

$3  +1.816 
.710     2.208 
.335      2.600 
7.958      2.991 
[7-579]     3.3§o 
3-769 
4-157 


18.293 
18.044 
17.790 
17.531 
17- 


2.7Q1 
3.l8t) 
3.568 
3-956 

4-343 


22.S97 

22.806 

22.710 
22.606 

22 
22, 


22.553 

22.000 
22.760 
22.854 
22.941 


6.643 
7.021 

7.398 

773 

147 
18 


18.500 

18.752 

I 

19.241 
19476 

19.706 
19.930 
20148 

20.359 
20.565 


23-321 
23-360 
23-393 
23419 
23-437 


12472 
12.141 
11.806 
11468 
11.128 


10-343 
10.701 
11.056 
II40Q 
11.758 


20.764 
20-957 
21.143 
21.323 

21 

21-001 


20-953 
21.130 
21.300 
21464 
21.623 
21.775 
21.920 


23405 
23.376 
23.340 
23.297 
23.247 
23.191 


21.661  0 

21.820  1 

21.972  2 

22.nS  3 

22.255  4 

22.386  5 

22.509  6 

22.626  7 

22.: 


0.550  11.175 


23.283  15 

23.331  16 

23.371  17 

23.403  18 

23.428  19 

23.444  20 

23453  21 

23-454  22 

23.447  23 

23432  24 

23409  25 

23-379  26 

23-341  27 

23.294  28 

2^.241  29 

23.179  30 

23.109  31 


44,  6.  Equation  of  Time  in  Minutes  and  Seconds  at  Greenwich  Mean  Noon  for  1891. 

Day  Jan,      Feb.     March     April     May      June      July    August   Sept,      Oct.      Nov.        Dec,  Day 


0    ™  1*6 

m    s 
13  40 

m    s 

12  45 

m  s 
H-4  17 

in  s 
o   -1 

m   s 

-2  35 

111     8 

3  20 

111    8 

6  10 

m   8 
H-o  15 

m  s 
959 

m  s 

16  18 

m  s 
—II   14       0 

1     345 

1348 

12  33 

359 

3  32 

6    7 

-0    4 

10  18 

16  20 

io  52      1 

a    4  13 

13  56 

12  21 

3  4i 

3    o 

2   lo 

3  44 

0    3 

0  23 

10  37 

16  21 

io  29     2 

3     4  41 

14     2 

12     8 

323 

3  13 

2     8 

3  55 

5  55 

042 

10  56 

16  21 

io    5     3 

4     5    8 

14    8 

"  55 

3    5 

3  19 

I  58 

4    6 

5  54 

I     I 

II  14 

16  20 

941     4 

5     535 

14  13 

II  42 

-+-2  48 

3  25 

-     48 

4  17 

548 

—I  21 

n  32 

16  19 

—  9  17     5 

662 

-14  18 

!I   28 

2  30 

37 

4  27 

5  42 

1  41 

ii  50 

16  io 

851      6 

7     628 

14  21 

II    14 

2  13 

3  34 

26 

4  37 

5  35 

2     I 

12    7 

16  13 

8  26     7 

8     654 
9     7  19 

14  24 
1426 

1059 

10  44 

150 

i  39 

338 
3  41 

l\ 

447 
456 

528 
520 

2  21 
242 

12  24 
12  40 

16   9 
16   5 

7  59     8 
733     » 

.0     7  44 

1427 

10  29 

-f-i  23 

344 

-051 

5    5 

5  12 

-3   3 

12  56 

15  59 

-7    6   10 

11     8    8 

14  28 

10  13 

i    7 

346 

039 

5  13 

5    3 

3  23 

13  12 

15  53 

6  38   11 

12     8  32 

1427 

9  57 

o  si 

348 

027 

5  21 

453 

3  44 

13  27 

1545 

6  io   12 

13     854 

14  20 

940 

035 

349 

o  15 

5  28 

443 

4    5 

13  41 

5  42   13 

14     9  17 

14  24 

924 

0  2O 

349 

—  02 

5  35 

432 

427 

1355 

152? 

513   14 

15     938 

14  22 

g    7 

+o    5 

349 

+0  10 

5  42 

421 

-448 

14    9 

15  19 

—  445    15 

16     959 
17     10  iq 

14  18 
14  14 

8  50 

8  32 

—  o  10 

o  24 

348 
3  47 

023 
o  36 

548 
5  53 

y 

5    9 
5  30 

14  22 
1434 

15   8 
14  57 

4  16    16 
346   17 

18    10  38 

14    9 

8  15 

o  38 

3  45 

049 

5  58 

3  43 

14  46 

14  44 

3  17   18 

19    1057 

14   3 

757 

052 

343 

I      2 

6     2 

3  30 

i  13 

1458 

14  3i 

247   19 

20    n  15 

1357 

739 

-     5 

3  40 

"*"1  IS 

6    6 

3  16 

g  34 

15    8 

14  17 

—  2  18  20 

21    n  32 

13  50 

7  21 

18 

3  37 

I   28 

6    9 

3    i 

6  ss 

15  18 

14    3 

148  21 

22    n  48 

1343 

I    3 

30 

3  33 

I  40 

6   12 

2  46 

716 

15  27 

13  47 

i  78   22 

23    12    4 
24    12  19 

13  20 

42 
53 

329 
3  24 

6  14 
6i5 

2  31 
2  15 

737 
758 

15  36 
15  44 

1331 
13  13 

048   23 
—  o  18   24 

25    12  33 

13  16 

6   8 

—2    4 

3  18 

+2  19 

6  16 

i  59 

-8  19 

IS  51 

12  55 

-»-  o  12   25 

26    12  46 
27    12  58 

13    6 

12  56 

5  49 
53i 

2  15 
2  2S 

3  12 
306 

231 
2  44 

6  17 
6  16 

53 

§39 
8  59 

j^57 

12  37 
12  17 

042   26 
i  12   27 

28    13  10 
29    1321 

12  45_ 
[12  33] 

5  12 
454 

234 
2  43 

2  S9 
2  52 

256 

3    8 

6  16 
614 

i    9 
o  51 

9  19 
9  39 

16  12 

ii  36 

141    28 
a  n   29 

30    13  31 
31    13  40 

435 
4  17 

251 

2  44 

2  35 

3  20 

6   12 

6  10 

033 
o  15 

959 

16  15 
16  18 

ii  14 

a  40  30 

3Q    31 

896 


Astronomical  Data. 

44,  H.    Solar  System. 


Tables  44  H,  45. 


Mercury 

87.97 

.387 

0.07? 

58. 

4.8 

0.4? 

6.? 

Venus  . 

224.70 

•723 

0.8? 

1  08. 

12.2 

5-? 

6.? 

Earth   . 

365.26 

I.OOO 

1.  00 

149. 

12.74 

6.1 

5-6 

Moon   . 

27.32 

.0026* 

O.OI2 

*o.39 

348 

0.07 

3-4 

Mars  .  . 

686.98 

1.524 

O.I  I 

227. 

0.7 

4- 

Jupiter  . 

4332.53 

5.203 

310. 

777- 

142.' 

1900. 

Saturn  . 

10759.22 

9-539 

93- 

1424. 

119. 

570. 

0.7 

Uranus 

30686.82 

19.18 

14. 

2864. 

50. 

85. 

Neptune 

60126.71 

30.05 

4487. 

60. 

100. 

0.9 

*  Distance  from  the  Earth. 

45.   Mean  Position 

of  Fixed 

Stars,  Jan.  0  1891. 

Names 

a 

0) 

<u 

1 

3% 

I 

ja 

c 
_© 

Gfl 
JS 

Designation 

'c 

.2?  c' 

U 

.S 

s 

00 

S  w 

X 

"o 

>> 

i 

< 

1 

u 
Q 

*E 
• 

o 

>• 

> 

i 

m     s 

s 

0 

O 

Sirrah 

a  Andromedae 

2 

0 

2  45.2+3.09 

4-28.489'- 

-.0055 

Polaris 

«  Ursae  Minoris 

2 

I 

18  53.4     2.36  +88.727  +.0053 

— 

«  Arietis 

2 

2 

i     1.7 

3.37  - 

4-22.947- 

^.0048 

Aldebaran 

a  Tauri 

I 

4 

29  39.9 

3.44- 

-(-16.289- 

-.0021 

Capella 
Rigel 

«  Aurigae 
p  Orionis 

I 
I 

5 

5 

8  38.2 
9  l7-9 

443  - 
2.88- 

-j-45.886- 
-  8.328- 

-.00  1  1 
-.0012 

Beteigeuze 

«  Orionis 

I 

5 

49  1  6.2 

3.25- 

f  7.386  +.0003 

Canopus 
Sirius 

a  Argus 
a  Canis  Majoris 

I 

I 

6 
6 

21  31.9 
40  20.6 

1-33  —52.636—  .0005 
2.64  —  i6.t;67i—  .00  u 

Castor 

a2  Geminorum 

2-1 

7 

27  38.7 

3.84  - 

-32.127  —  .0021 

Procyon 

a  Canis  Minoris 

1     7 

33  35-7     3-H  - 

-    5.504—  .0025 

Pollux 

p  Geminorum 

1-2  7 

38  38.7    3.68  ;- 

-28.289'  —  .OO23 

Regulus 

a  Leonis 

I-2;IO 

2    34.0       3.20- 

-12.500—  .0049 

Denebola 

p  Leonis 

2    II 

43  30.0,     3.06  - 

•-15.181  —  .0056 

— 

a  Crucis 

I    JI2 

20   32.6;      3.30  - 

-62.49  5  -.005  6 

Spica 

a  Virginis 

I     13 

19  27.0:    3.15  —io.592|-.oo53 

— 

p  Centaun 

1    J3 

56    8.O|    4.18  —59.8471  —  .0049 

Arcturus 

«  Bootis 
a2  Centauri 

!-3 

10  41.3:    2.73  j- 
32  12.5;    4.04  - 

fi9.75o|—  .0053 
—60.383  —  .0042 

Antares 
Vega 
Altair 
Deneb 
Formaihaut 
Markab 

«  Scorpii 
«  Lyrae 
a  Aquilae 
«  Cygni 
«  Piscis  Aust. 
a  Pegasi 

1-2 
I 
1-2 
2-1 
1-2 
^ 

16 
18 
19 

20 
22 

22 

22   43.4       3.67    -26.189—  .0023 

33  14.8     2.03  +38.683  +.0009 
45  27.9     2.93  |4-  8.581  +.0026 
37  42.9     2.04  +44.89  1  +.0035 
*i  37-6     3-32  i—  30.200+0053 
59  19.8+2.98  +I4.6i9+.oo54 

Note.  Tho  yearly  precession  of  the  equinoxes  is  about  so".25,  or  o°.oo245-*- 
The  mean  (not  apparent)  obliquity  of  the  ecliptic  for  1891  is"  about  23°,  27',  13"^ 
or  27°.453.  The  :nean  obliquity  decreases  annually  by  o".8,  or  o°.ooo2. 


tables  46— 48.  Latitude,  Longitude  and  Gravity. 


897 


46.    Latitudes  and  Longitudes 

Latitude  Longitude  Elevation 
o  h  ra    s         Metres 

Aberdeen   .    .    .057.149  No    8  23  W 
Amsterdam    .    .  T  52.371  N  O  19  39  E 
Antwerp         .    .  T5I.22I  N  O  17  37  E 
Athens.        .    .  637.972  N  I  34  55  E 
Baltimore      .    .  T  39.298  N  5    628W        55 
Belfast.        .    .       54.66    N023..W 
Berlin    .        .    .  O  52.505  N  O  53  35  E          40 
Bonn     .        .    .       50.729  N  O  28  23  E          50 
Boston.       .   .T42.358N  44415  W       63 
Brussels         .    .       50.853  N  0  17  29  E          90 
Calcutta        .    .T  22.557  N  5  53  19  E         39 
Cambridge  U,  S.  O  42.380  N  4  44  31  W 
Cambridge  Eng,.  052.215  N  O    O  23  E 
CapeofGoodHope  O  33-934  S  I  13  55  E 
Christiania     .    .  059.912  N  042  54  E          42 
Copenhagen  .    .  O  55.687  N  0  50  19  E          53 
Cork     .    .    .    .T  51,90    No  33  51  W 
Dublin.    .    .    .  053.387  N  02521  W  T  24 
Edinboro    .    .    .  O  55.956  N  O  12  43  W  Tl39 
Geneva ....      46.200  N  O  24  37  E 
Genoa  .    .    .    .  T444I9  N  0  35  41  E 
Glasgow    .    .    .  055.879 N  017  ii  W 
Gottingen  .    .    .      51.530  N  O  3946  E        130 
Greenwich.    .    .051.477  No    0    o        T  64 
Heidelburg     .    .      49.40    N  O  34  32  E        IOO 
Leipzic.    .    .    .      51.335  N  o  49  34  E        100 
Lisbon  .    .    .    .  O  38.705  N  O  36  34  W 
Liverpool  .    .    .  O  53.401  N  O  12  17  W 
Magnetic  Pole  .      77.83    N  4  14       W 


Measured  from  Greenwich. 


Latitude  Longitude  Elevation 
o      h  m  s   Metres 

50 
663 


51.514  N  o  023\V 
O  40.408  N  01445  W 

53.48   N  o  9..  W 

37.83iS    9  39  54  E 
T  45.52   N  4  54  13  W 

48.146  N  04626E 
O 40.863  N  057    i  W 
T29.963N  6   OHW 
O  40.730  N  45557  W 
O  48.836  N  o   921  E 


44 
525 


London    . 
Madrid    . 
Manchester 
Melbourne 
Montreal . 
Munich    . 
Naples     . 
New  Orleans 
New  York. 

Paris.  .  .  O  48.836  N  O  92iE  60 
Philadelphia.  T 39.95 3  N  5  o  39  W  50 
Quebec  .  .O  46.805  N  44449X^X108 
Queenstown.  T  51.85  N  0  33  6  W 
Rio  deJaneiro  O  22.907  S  2  52  41  W  T  69 
Rome.  .  .  41.898  N  04954E  29 
Rotterdam  .  T  5 1.908  N  o  17  55  E  28 
San  Francisco  O  37.790  N  8  9  43  W  Ti  1 1 
Savannah.  .  T 32.081  N  5  24  21  W  42 
St.John(N,S.)  T 45.262  N  4  24  15  W  38 
StPetersburg  O  59.942  N  2  I  14  E  II 
Stockholm  .  O  59.343  N  I  12  14  E  20 
048.582 N  031  2E  150 
033-861810  45oE  T  65 
045.643 N  055  2E  T  17 
O  45.430  N  04925E 
48.210  N  i  532E  182 


Strassburg 
Sydney  . 
Triest.  . 
Venice  . 
Vienna  . 
Washington 
Wellington 


O38.894N  5   8i2WT  63 
T4I.288S  ii  39  ii  E    T  18 


[Note.  T  =  Time  Signal.    O  =  Observatory 


47.   Acceleration  of  Gravity  in 

Lat.  +0°  -j-l°  +  2°  +3° 
0°  978.10  978.10  978.11  978.12 
978.25  978.29  978.32  978.36 
978.69  978.75  978.81  978.87 

979-35  979-43  979.51  979-59 
980.17  980.26  980.34  980.43 
981.04  981.13  981.21  981.30 
981.86  981.93  982.01  982.08 
982.52  982.58  982.63  982.68 
982.96  982.99  983.01  983.03 


10° 
20° 
30° 
40° 
50° 
60° 
70° 
80° 


Different  Latitudes  (cm.  per  sec.  per  sec.)-* 

+  4°    +5°    -f-6°    H-7°    +8°    +9°   Dif 

978.13  978.14  978.16  978.18  978.20  978.23  l 

978.40  978.44  978.48  978.53  978.58  978.63  4 

978.93  979.00  979.06  979.13  979.21  979.28  7 

979.67  979.75  979.83  979.92  98o-00  980.09  3 

980.52  980.61  980.69  980.78  980.86  980.95  9 

981.38  981.46  981.54  981.62  981.70  981.78  8 

982.15  982.21  982.28  982.34  982.41  982.47  7 

982.73  982.77  982.82  982.86  982.89  982.93  4 

983.05  983.07  983.08  983.09  983.10  983.11  ! 


Dif 


48.    Length  of  Seconds-Pendulum  in  Different  Latitudes  (cm.).* 
Lat.  -f  0°    +1°    -f-2°    +3°    +4°    +5°    +6°    +7°    +8°    +  9° 
0°   99.103  99.103  99.103  99.104  99.105  99.106  99.108  99.110  99.112  99.115   i 

10°  99.118  99.121  99.125  99.128  99.132  99.137  99.14!  99.146  99.151  99.156  4 

20°  99.162  99.168  99.174  99.180  99.187  99.193  99.200  99.207  99.214  99.222 

30°  99.229  99.237  99,245  99.253  99.261  99.269  99.278  99.286  99.295  99.303 

40°  99.312  99.321  99.330  99.338  99.347  99.356  99.365  99.374  99.383  99.391  9 

50°  99.400  99.409  99.418  99.426  99.435  99443  99-45 *  99-459  99.467  99-475  s 

$0°  99.483  99.491  99.498  99.505  99.512  99.519  99.526  99.532  99.539  99-545  7 

70°   99.550  99o56  99.561  99.566  99.571  99.576  99.580  99.584  99.588  99.591    4 
80°  99.594  99-597  99.600  99.602  99.604  99.606  99.607  99.608  99.609  99.010   i 

*  These  values  are  calculated  for  the  sea  level.  A  deduction  of  0.03  %  should  be 
made  for  each  kilometre  of  elevation  above  the  ground  and  a  deduction  of  0.02%  should 
be  made  for  each  kilometre  of  elevation  of  the  ground  above  the  sea. 


898 


Reduction  of  Measures. 


Table  49a 


49a.  Reduction  of  Measures  to  and  from  the  C.  G.  S.  System. 

Lengths  in  centimetres  Equivalent  Logarithm       Reciprocal 

inch =  2.53997  0.40483  .393705 

link  =  7.92  in =  20.1165  1.30355  -0497103 

foot  =  12  in.  .    .    .    .    .    •    .  =  30.4796  1.48401  .0328088 

yard  =  3  ft.    ....'...  =  9M389  1.961 13  .0109363 

fathom  =  6  ft =  182.878  2.26216  00546813 

rod  =  i6'/8  ft —  502.914  2.70149  .00198841 

chain  =  100  links  =  66  ft. .    .  =  2011.65  3-30355  .000497103 

statute  mile  =  5280  ft.     .    .    .  =  160,932  5.20664  6.21378x10-* 

nautical  mile =  185,200(7)  5.2676    5.40x10-6 

A  eas  in  square  centimetres 

square  inch .    .  =  6.4514  0.80966  .15500 

square  foot  =  144  sq.  in.    .    .  —  929.01  2.96802  .0010764 

square  yard  =  9  sq.  ft.   .    .    .  =  8361.1  3.92226  .00011960 

acre  =  43,560  sq.  ft =  4.0468x10?  7.60711  2.4711x10-8 

square  mile  =  640  acres     .    .  =:  2.5899XI010  10.41329  3.8611x10—" 

Vilumea  in  cubic  centimetres 

cubic  inch —  16.386  1.21449  .061026 

cubic  foot  =  1728  cu.  in.    .    .  =  28316  445203  3.5316x10-5 

cubic  yard  =  27  cu.  ft.  .    .    .  =  764526  5.88339  i  3080x10-6 

U.  S.  pint  =   1.043  Ibs.  water  =  473  2.6750    .002114 

U.  S.  quart  =  2  pints  .    .    .    .  =  946  2.9760    .001057 

dry  quart =  noi  3.0418    .000908 

U.  S.gallon  =  231  cu.  in.  =  4  qts.  =  3785  3-578i    .0002642 

imperial  gallon  =  10  Ibs.  water  =  4541  3.6572    .0002202 

Masses  in  grams 

grain ;   ..  =  .0647987  2.8115715.4324 

ounce  (Avoirdupois)  =  Vie  H>»  =  28.3494  1.45254  .0352741 

ounce  (Troy)  =  480  grams      .  =  31.1034  1.49281  .0321509 

pound  (Troy)  =  12  oz.  Troy.  =  373-240  2.57199  .00267924 

pound  (Avoir)  =  7000  grains  />a*  453,590  2.65666  2.20463x10—3 

English  ton  =  2240  Ibs.  .    .    .  ±r  1.01604x10*  6.00691  9.84210x10-7 

Times  in  mean  solar  seconds 

year  (tropical)  =  365.24222  days  =  31,556.928  7.49809  3.i6888xio-8 

sidereal  year   =  365.25637  days  =  31,558,150-  7.49811  3.16875x10-* 

(mean  solar)  day =  86,400  4.93651  .000011574074 

hour =  3,6oo  3-5563o  .00027777778 

minute =  60  1.77815  .016666667 

so-called  sidereal  second      .    .  =  0.9972695666  £.99881  1.0027379091 

true  sidereal  second     .    .    .    .  =  0.9972696721  1.99881  1.0027378030 

Velocities  in  centimetres  per  second 

kilometre  per  hour =  27.7778  1.4437°  .0360000 

foot  per  second —  30-4796  1.48401  .0328088 

mile  per  hour =  44-7°33  1.65034  .0223696 

nautical  mile  per  hour    ...  =  51.44  1.7113     .01944 

kilometre  per  minute  .    .    .    .  =  1666.67  3.22185  .0006000000 

mile  per  minute —  2682.20  3*42849  .000372827 

Accelerations  in  cm.  per  sec.  per.  sec. 

foot  per  sec.  per  sec =  30.4796  1.48401  .0328088 

Densities  in  grams  per  cu.  cm. 

grain  per  cubic  inch =  .0039544  3.59708  252.88 

Ib.  per  cubic  foot    .....=  .016019  2.20463  62.426 

Heat  TJnits  in  ergs. 

unit  of  heat  =  i  gram-degree  G.  •=  4.T7XIO7  7.620      2.40x10-8 

Ib.-degree  Fahrenheit  .    .    .    .  =  i.o5ixio10  10.022      9.52x10-" 

i  Ib.-degree  Centigrade  .    .    .    .  —  1.89X10*°  10.277      5.29x10- » 

i  Calorie   =  1000  g° =  4.i7Xio10  10.620      2.40x10-" 


Reduction  of  Measures. 


Table  49b 

49  b.  Continuation.  Reduction  of  Measures  to  and  from  the    C.  G.  S.  System. 

Values  marked  with  an  asterisk  (*)  are  independent  of  the  acceleration  of  gravity  (g). 

11H1 

_!  ^J-O   O   O   O   O 

99    t^oAAAAA* 


899 


00          O 

0»     ^2 


it  1  1 

- 


xxxx 

c,    ON  O   *t-  ^1 
O  O 


MMO 

~ 


PC  l-<     r}-OO    HH    i-  OO 
O    ON  »*• 

oq  CJN  ^ 
,  M  ri  rt-  1/>  vno    0 


f'>vo"vo"<O  S  VO*  t^.C»   O  ^0 


OO    ONON<S    COONO    O 
VO    ONONHHOO    ONO    O 


NO  VO 


900 


Constants. 


Table  50. 


1.427 


Gravity.    Attraction  between  two  unit    .  .  .  . 
masses  (i  g)  at  unit  distance  (i  cm.)  in  dynes 


Seconds-pendulum  (lat  45°)  in  cm 99.3 

i  gram  (lat.  45°)  in  dynes 

Atmospheric  mean  molecular  weight 

„    Pressure  (76  cm.  Paris)  in  megadynes  per  sq.  cm. 


.  6.5X10-* 


1360 


Density  of  Air,  (o°,  76  cm.  Paris)       0.0012932 

„    (o°,  i  megadyne  per  sq.  cm.).  ....  00012^59 
Hydrogen  (o°, 


.  70  cm.  Paris) 
(o°,  i  megadyne  per  sq.  cm.)  . 

Water  at  4° 1.00001 

„     apparent  at  21° 0.997 

Crown  glass,  about 2.5 

Brass  „        84 

Mercury  at  19* I3-55Q 

Sonnd  Velocity  in  dry  air  at  o°  in  cm.  per  sec.  33,220  or  33,200 
i  mean  semitone  involves  ratio  JY2 1-059463 


5.95216 

"5.94630 

O.OOO004 


4.521 
0.02509 


.3183099 
.1013212 

.5641896 
.7071008 


50.  Numbers  Frequently  Required  in  Calculation. 
Mathematical  Constants.  Number  Logarithm  Reciprocal. 

Ratio  ot  circumference  to  diameter   ....  n  = 

Square  of  Ditto TI*  = 

Square  Root  of  Ditto VTI  =:  1.7724539 

Square  Root  of  2 y2   =  14142136 

Square  Root  of  3 V3   =  1.7320508 

Square  Root  of  10 Vio  =  3-1622777 

Logarithmic  Base     f   =  2.7182818 

Logarithmic  Modulus M  —  04342945 

I  degree  in  circular  measure 1°  =  -01745329 

i  minute  in  circular  measure i'    =  .00029089 

i  second  in  circular  measure I*  r=  .00000485 

Probable  error  (mean  error  =  i) 0^7449 

Astronomical  Constants. 

Sidereal  time  in  Mean  time 0.9972696 

i  (tropical)  year  —  See  Table  49  —  in  days  ....  365.24222 
Annual  precession  of  equinoxes  (5o".25)  in  days  .  .  0.01415 

Aberration  constant  (20*45)  in  degrees 0.00568 

Sun's  mean  angular  semidiameter  (16'  2")  in  degrees  0.267 
">olar  parallax  (8" .83?)    .  . .00245 

earths  equatorial  radius  in  kilom 6378. 

"    ths  polar  „        „       „       6356.+ 


.31022' 

.3678794 

2.302585 

57-2957 

3437-747 


i 

1.0027379 

0.0027379 

7o£ 

176. 

3-74 

408. 

.0001568 

.0001573 

I.54XIO* 

.010065 

.0010198 


1116.1. 

11310. 

0-99999 

1.003 

040 

.119 

.073800 


Light.    Velocity  in  cm.  per  sec 3-ooXio10 

sodium,  wave  length  in  air  icm.) .00005893 

Refractive  Index  of  water  for  ditto 1.333 

Dispersive      .,       „       „       „       „          0.0144- 

Rotation  of  ditto  by  Quartz  plate  i  cm.  thick  .  .  .  217° 

Candle  power  of  i  sq.  cm.  melted  platinum  (2  Carcels)  20 

Heat.    Conductivity  of  Copper  C.  G.  S 0.9+ 

Coefficient  of  Expansion  of  glass  (cubical) 000025 

„  „          „  „  steel  (linear) .000012 

„  „          „  „  brass     „          .000019 

„  „          „  „   mercury  (cubical  20°) .  .000180-4- 

„  „          „  „   gases  .00367 

Latent  Heat  of  Water 79 

„       „  Steam  (100°,  76  cm.) 536 

Specific  Heat  of  Brass 0^04 

„          „     „    Glass ai9 

„          „     „    Water  (o°— 100°) i-oos 

„     „    Air  (o°— 100°,  76  cm)  0.2383  or.  .  .  0.238 

„      „    Gases,  (ratio  of  2  Sp.  Hts.).  .  .  .  1.408 

Mechanical  Equivalent  of 

i  unit  of  heat  (i  g°)  in  ergs,  4.166X10'  or. 4.i7Xio7      7.620 

i  kilogrammetre  (lat.  45°) 9.8061  Xio7  7.99149 

i  foot-pound       (  „     „ )  „ i.3557Xio7  7.13217 

Electro-Chemical  equivalent  of  Hydrogen 

in  grams  per  ampere  per  sec .00001038      5.0162 

i  Electrostatic  Unit  of  E.  M.  F.  in  volts 300  2477 

Electromotive  Force  of  Daniell  cell  in  volts    ...  i.oto  1.2     0.00  to  0.08 

Internal  Resistance  of  Quart  „       „     „   ohms  ...  ito2  0.0  to  0.3 

I  B.  A.   unit  in  legal  ohms 0.9889          J-9952 

i  Siemens  „    „       ,,         „        0.0434  1^9747 

Specific  Electrical  Resistance  of  Mercury  (C.  G-S.)  o.942Xio5    4.974 


Magnetic  susceptibility  of  iron    . 
'lotal  Intensity  of  Earths  Field 


LStoTS 


240X10-8 
1.0198x10-8 

7.376X10-  -» 
9634 

•00333  0 

IJO  to  08 

i  .o  to  .5 

I.O1I 

1.060 
1.061X10—  • 

•003? 
3  to  1.5 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN     INITIAL    FINE      OF     25     CENTS 

OVERDUE. 

= 

SEP    12 
FEB  26  1935 

l;    S:PJ371837 
MAR  29  1944 
DEC 


YC   I  1 352 


v?  • 


ft. 


. 


